**Ray Optics Questions and Answers**

Below are some of the very important NCERT Class 12 Physics Chapter 9 Ray Optics Questions and Answers. These Class 12 Ray Optics Questions and Answers have been prepared by expert teachers and subject experts based on the latest syllabus and pattern of term 2 questions with answers to help students understand the concept.

These Questions for** **Class 12 Physics Ray Optics Questions and Answers are very important for the latest CBSE term 2 pattern. These Class 12 Q and A are very important for students who want to score high in CBSE Board.

We have put together these NCERTQuestions of Class 12 Physics Chapter 8 Electromagnetic Waves Questions and Answers for practice on a regular basis to score high in exams. Refer to these Questions with Answers here along with a detailed explanation.

**Short Answer (SA) Type Questions**

**1. When monochromatic light travels from a rarer to denser medium, explain the following, giving reasons.**

**(i) Is the frequency of reflected and refracted ray same as the frequency of incident light?****(ii) Does the decrease in speed imply a reduction in the energy carried by light wave?**

**2. Mention any two situation in which Snell’s law of refraction fails.**

**3. A ray of light is incident at an angle of 45 ^{o} on one face of rectangular glass slab of thickness 10 cm and refractive index 1.5. Calculate the lateral shift produced.**

**4. Why does the sun rising in the sky appear oval in shape?**

**5. Show analytically from the lens equation that when the object is at the principal focus, the image is formed at infinity.**

**6. Astudent measures the focal length of a convex lens by putting an object pin at a distance ‘u’ from the lens and measuring the distance ‘v’ of the image pin. What will be the graph drawn between ‘u’ and ‘v’.**

**7. A magician during a show makes a glass lens n = 1.47 disappear in a trough of liquid. What is the refractive index of the liquid? Could the liquid be water?**

**8. A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index of water? If water is replaced by a liquid of refractive index 1.63 upto the same height, by what distance will the microscope have to be moved to focus on the needle again?**

**9. What should be the position of the object relative to the biconcave lens, so that this lens behaves like a magnifying glass?**

**10. How does the magnification of a magnifying glass differ from its magnifying power?**

**11. Calculate the radius of curvature of an equi-concave lens of refractive index 1.5, when it is kept in a medium of refractive index 1.4, to have a power of -5D.**

**12. An equi-concave lens of focal length ‘f’ is cut into two equal halves in thickness. What is the focal length of each half?**

**13. What is the focal length of convex lens of focal length 30 cm in contact with a concave lens of focal length 20cm? Is this system a converging or diverging lens? Ignore thickness of the lenses.**

**14. The figure shows a ray of light falling normally on the face AB of an equilateral glass prism having refractive index 3/2, placed in water of refractive index 4/3. Will this ray suffer total internal reflection on striking the face AC. Justify your answer.**

**15. A ray PQ incident normally on the refractive face BA is refracted in the prism BAC made of material of refractive index 1.5. Complete the path of rays through the prism.**

**From which face will the ray emerge? Justify your answer.**

**16. An equilateral glass prism has a refractive index 1.6 in air. Calculate the angle of minimum deviation of the prism, when kept in a medium of refractive index (4√2)/5.**

**17. Is it possible to increase the range of telescope by increasing the diameter of the objective lens?**

**18. Explain two advantages of a reflecting telescope over a refracting telescope.**

**19. Small telescope has an objective lens of focal length 144 cm and an eyepiece of focal length 6 cm. What is the magnifying power of the telescope? What is the separation between the objective and the eyepiece?**

**20. The objective of an astronomical telescope has a diameter of 150 mm and a focal length of 4 m. The eyepiece has a focal length of 25 mm. Calculate the magnifying power of telescope (λ = 6000 A ^{o} for yellow colour).**

**21. Define power of a lens. Write its units. Deduce the relation for two thin lenses kept in contact coaxially.**

**22. A symmetric bi-concave lens of radius of curvature R and made of glass of refractive index 1.5, is placed on a layer of liquid placed on top of a plane mirror as shown in the figure below.**

**An optical needle with its top tip on the principal axis of the lens is moved along the axis until it’s real and inverted image coincides with the needle itself. The distance of the needle from the lens is measured to be ‘x’. **

**On removing the liquid layer and repeating the experiment the distance is found to be ‘y’. Obtain the expression for the refractive index of the liquid in terms of ‘x’ and ‘y’.**

**23. State the condition of total internal reflection. Refractive indices of the given prism material for red, blue and green colours are 1.39, 1.48 and 1.42 respectively. Trace the path of rays through the prism.**

**24. A ray of lightincident on the face AB of an isosceles triangle prism makes an angle of incidence ‘i’ and deviates by angle as shown in the figure. Show that in the position of minimum deviation ∠β=∠α. Also find out the condition, when the refracted ray QR suffers total internal reflection.**

**25. (i) A ray of light incident of face AB of an equilateral glass prism, shows minimum deviation of 30 ^{o}. Calculate the speed of light through the prism.**

**(ii) Find the angle of incidence at face AB, so that the emergent ray grazes along the face AC.**

**26. An optical instrument uses and optic objective lens of power 100 D and an eyepiece of power 40 D. The final image is formed at Infinity when the tube length of instrument is kept at 20 cm. Identify the optical instrument. Calculate the angular magnification produced by the instrument.**

**27. Draw a labelled ray diagram of an astronomical telescope in the near point adjustment position. A giant refracting telescope at an observatory has an objective lens of focal length 15 m and an eyepiece of focal length 1 cm. If this telescope is used to view the moon, find the diameter of the image of the moon formed by the objective lens. The diameter of the moon is 3.48 x 10 ^{6} m and the radius of lunar orbit is3.8 x 10^{8} m.**

**Short Answer Type Question Answer**

1. (i) The frequency of reflected and refracted light remains same as that of the incident light because frequency only depends on the source of light.

(ii) Since, the frequency remain same, has there is no reduction in energy.

2. Snell’s law of refraction fails in 2 situations

(i) when total internal reflection takes place at an angle greater than the critical angle

(ii) when light is incident normally on the surface

3. Given i = 45^{o}, t = 10 cm = 0.1 m and μ = 1.5

By Snell’s law, μ = (sin i / sin r)

sin r = sin i / μ = sin45^{o} / 1.5 = 0.4713

r^{-1} = sin^{-1}(0.4713) = 28.12^{o}

Lateral shift = (tsin(i – r)) / (cos r) = [0.1 x sin (45^{o} – 28.12^{o})] / cos 28.12^{o}

Lateral shift = 0.033 m

4. It is due to the refraction of sunlight as it travels through different layers of the earth’s atmosphere. Refraction of light by these layers can make the sun appear flattened or distorted. The rays of light from the upper part and lower part of the periphery of the sun bend unequally on the traveling through Earth’s atmosphere, making the sun appear oval in shape.

5. Given u = -f

From lens maker’s formula

6.

7. If μ_{1} = μ_{2}, then f = ∞

Hence the lens in the liquid arts like a plane sheet, when refractive index of the lens and the surrounding medium is the same. Therefore, μ_{1} = μ_{2} = 1.47. Hence the liquid medium is not water. Refractive index for water is 1.33.

8. **Case 1** : When tank is filled with water.

Given, the apparent depth = 9.4 cm

Height of water, t = 12.5 cm

Real depth = 12.5 cm

Refractive index of water, μ_{w} = (Real depth / Apparent depth) = 12.5 / 9.4 = 1.33

**Case** **2** : When tank is filled with the liquid.

Refractive index of the liquid, μ_{l} = (Real depth / Apparent depth)

Apparent depth = 12.5 / 1.63 = 7.67 cm

Therefore, The microscope is shifted by 9.4 – 7.67 = 1.73 cm.

9. Whenever object is placed within the focus of the bi-concave lens, we will obtain enlarged image, hence the by concave lens behaves like a magnifying lens.

10. The magnification of a magnifying glass depends upon, where it is placed between the user’s eye and the object being viewed and the total distance between them, while the magnifying power is equivalent to angular magnification.

11.

12.

13. Given, focal length of convex lens, f_{1} = 30 cm

Focal length of concave lens, f_{2} = -20 cm

Using the formula of combination of lens

1/f = 1/f_{1} + 1/f_{2} = 1/30 -1/20 = -1/60

f = – 60 cm

Since, the focal length of combination is negative in nature, so, the combination acts like a diverging lens, i.e. as a concave lens.

14. Given refractive of water, μ_{w} = 4/3

Refractive index of glass prism, μ_{g} = 3/2

For total internal reflection occurrence the incident angle must be greater than critical angle.

As the critical angle 61.6^{o} is greater than the angle of incidence 60^{o}, TIR will not occur.

15. Given refractive index of the material of the prism, μ = 1.5

From the ray diagram it is clear that angle of incidence i = 30^{o} < C.

Therefore, the ray incident at the face AC will not suffer TIR and merges out of this face.

16.

17. By increasing the diameter of the objective lens, we can increase the range of the telescope because as the diameter of the lens increases, the area covered by the lens also increases. Lens is able to focus on a large area thereby helping us to view the object better.

18. Advantage of reflecting telescope over refracting telescope are:-

(i) reflecting telescope image formed is free from chromatic aberration defect. So, it is sharper than image formed by a refracting telescope.

(ii) mirror is easy to produce with a large diameter so that it can intercept rays crossing a large area and direct them to the eyepiece.

19. Given, focal length of the objective lens, f_{o} = 144 cm

Focal length of eyepiece, f_{e} = 6 cm

Magnifying power of the telescope in normal adjustment,

m = -f_{o}/f_{e} = -144/6 = -24

Separation between lenses, L = f_{o} + f_{e} = 144 + 6 = 150 cm

20.

21. The power of a lens is equal to the reciprocal of its focal length, when it is measured in metre. Power of a lens, P = 1/f and its SI unit is dioptre (D).

Consider two lenses A and B of focal lengths f_{1} and f_{2} placed in contact with each other. An object is placed at a point ‘O’ on the focus of the first lens A.

The first lens produces an image at I, which serves as a virtual object for the second lens B producing the final image at I.

Since, the lenses are thin, we assume the optical centres P of the lenses to be coincident. For the image formed by the first lens A, we obtain

22. First measurement gives the focal length (f_{eq} = x) of combination of convex lens and the plano-convex liquid lens. Second measurement gives the focal length (f_{1} = y) of the convex lens.

Focal length (f_{2}) of plano-convex lens is given by

23. There are 2 conditions for total internal reflection as follows:

(i) Light must travel from denser to rarer medium.

(ii) Angle i > i_{c}

Therefore, angle of incidence at face AC is 45^{o} which is more than the critical angle for blue and green colours. Therefore blue and green colours will undergo total internal reflection but red colour will reflect to other medium.

24.

25. (i)

(ii)

26.

(i) Since the focal length of eyepiece is more than the focal length of objective, so the optical instrument is compound microscope.

(ii) Since the final image is formed at infinity, so the angular magnification is given by

27. The ray diagram of an astronomical telescope in the near point adjustment position is shown below.

**Long Answer (LA) Type Questions**

**1. (i) A point object ‘O’ is kept in a medium of refractive index n _{1} in front of convex spherical surface of radius of curvature ‘R’ with separates the second medium of refractive index n_{2} from the first as shown in the figure.**

**Draw the ray diagram showing the image formation and reduce the relationship between the object distance and image distance in terms of n _{1}, n_{2} and R.**

**(ii) When the image formed above acts as a virtual object for concave spherical surface separating the medium n _{2} from n_{1} (n_{2}>n_{1}), draw this ray diagram and write the similar (similar to (i)) relation. Hence, obtain the expression for the lens makers formula.**

**2. (i) Define the term focal length of a mirror. With the help of a ray diagram, obtain the relation between its focal length and radius of curvature.**

**(ii) Calculate the angle of emergence (e) of the ray of light incident normally on the face AC of a glass prism ABC of refractive index √3. How will the angle of emergence change qualitatively, if the ray of light images from the prism into a liquid of refractive index 1.3 instead of air?**

**3. (i) Under what condition is the phenomenon of total internal reflection of light observed? Obtain the relation between the critical angle of incidence and the refractive index of the medium.**

**(ii) Three lenses of focal length +10 cm, -10 cm and +30 cm are arranged coaxially as in the figure given below. Find the position of the final image formed by the combination.**

**4. (i) Two thin lenses are placed coaxially and contact. Obtain the expression for the focal length of this combination in terms of the focal length of the two lenses.**

**(ii) A converging lens of refractive index 1.5 has a power of 10 D when it is completely immersed in a liquid it behaves as a diverging lens of focal length 15 cm find the refractive index of the liquid.**

**5. A ray PQ of light is incident on the face AB of a glass prism ABC and emerges out of the face AC. Trace the path of the ray. Show that i + e = A + δ**

**where δ and e denote the angle of deviation and angle of emergence respectively. Plot a graph showing the variation of angle of deviation as a function of angle of incidence. State the condition under which ∠δ is minimum.**

**6. Define magnifying power of a telescope. Write its expression. A small telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. If this telescope is used to view a 100 m high tower 3 km away, find the height of the final image, when it is formed 25 cm away from the eyepiece.**

**7. Draw a ray diagram to show the working of a compound microscope. Deduce an expression for the total magnification, when the final image is formed at the near point.**

**In a compound microscope, an object is placed at a distance of 1.5 cm from the objective of focal length 1.25 cm. If the eyepiece has a focal length of 5 cm and the final image is formed at the near point. Estimate the magnifying power of the microscope.**

**8. How is the working of a telescope different from that of a microscope? The focal length of objective and eyepiece of a microscope at 1.25 cm and 5 cm, respectively. Find the position of the object relative to the objective in order to obtain an angular magnification of 30 in normal adjustment.**

**9. (i) Draw a labelled ray diagram showing the image formation of a distant object by refracting telescope.**

**Deduce the expression for its magnifying power when the final image is formed at infinity.**

**(ii) The sum of focal lengths of the two lenses of refracting telescope is 105 cm. The focal length of one lens is 20 times that of the other. Determine the total magnification of telescope with the final image is formed at infinity.**

**Long Answer Type Question Answer**

1. (i) Let a spherical surface separate a rarer medium of refractive index n_{1} from the second medium of refractive index n_{2}. Let C be the centre of curvature and R=MC be the radius of the surface.

Consider a point object ‘O’ or lying on the principal axis of the surface. Let a ray starting from ‘O’ incident normally on the surface along OM and pass straight. Let another ray of light incident on NM along ON and refract along NI. From M, draw MN perpendicular to OI.

The above figure shows the geometry of the formation of image ‘I’ of an object ‘O’ and the principal axis of a spherical surface with centre of curvature ‘C’ and the radius of curvature ‘R’. Here, we have to make following assumptions :-

(a) the aperture of the surface is small as compared to other distance involved.

(b) NM will be taken as nearly equal to the length of the perpendicular from the point N on the principal axis.

(ii) Now, the image I’ acts as a virtual object for the second surface that will form a real at I. As refraction takes place from denser to rarer medium,

2. (i) The distance of the principal focus from the pole of the mirror is called the focal length of the mirror.

Relation between focal length and radius of curvature of mirror :-

Considered a ray parallel to the principal axis striking the mirror at point M, then CM will be perpendicular to the mirror at point M.

Let Ө be the angle of incidence and MD be perpendicular to the principal axis.

(ii)

3. (i) Following are the criteria for total internal reflection.

(a) Light must pass from a optically denser to a optically rarer medium.

(b) Angle of incidence in denser medium is must be greater than critical angle for two media.

(ii)

4. (i)

5. (i) Let PQ and RS are incident and emergent rays and incident ray get deviated by δ by the prism. i.e. ∠TMS = δ

Let δ_{1} and δ_{2} are deviation produced at refractions taking place at AB and AC, respectively.

6. Magnifying power of a telescope is the ratio of the angle β subtended at the eye by the image to the angle α subtended at the eye by the object.

7. A compound microscope consists of two convex lenses co-axially separated by some distance. The lens nearer to the object is called the objective. The lens through which the final image is viewed is called the eyepiece. The focal length of objective lens is smaller than eyepiece.

The objective lens forms real and inverted magnified image A’B’ of object AB fall some, where between pole and focus of eye lens.

So, A’B’ acts as an object for eyepiece and its virtual magnified image A”B” formed by the lens.

The magnifying power of a compound microscope is defined as the ratio of the visual angle subjected by final image of eye and the visual angle subtended by object at naked eye, when both are at the least distance of distinct vision from the eye.

8.

CHARACTERISTIC | TELESCOPE | MICROSCOPE |
---|---|---|

Position of object | At infinity | Near objective at a distance lying between f_{o} and 2f_{o} |

Position of image | Focal plane of objective | Beyond 2f_{o}, where f_{o} is the focal length of objective |

9. It consists of an objective lens of a large focal length (f_{o}) and large aperture, also an eyepiece of small aperture and focal length.

(i) Magnification when final image is formed at infinity, magnification, m = -f_{o}/f_{e} and length of telescope, L = |f_{o}| + |f_{e}|

**Case Study Based Questions**

**1. Refraction involves change in the path of light due to change in the medium.**

**When a beam of light encounters and other transparent medium, a part of light gets reflected back into the first medium, while the rest enters the other. The direction of propagation of an oblique incident ray of light, that enters the other medium, changes at the interface of two media. This phenomenon is called refraction of light.**

**(i) For the same value of angle of incidence, the angle of refraction in three media A, B and C are 15 ^{o}, 25^{o} and 35^{o} respectively. In which medium, would the velocity of light be minimum?**

**(ii) Why does a crack in a glass window pane appear silvery?**

**(iii) The refractive index of diamond is much higher than that of glass. How does a diamond cutter make use of this fact?**

**(iv) What is the apparent position of an object below a rectangular block of glass 6 cm thick, if a layer of water 4 cm thick is on the top of the glass?**

**Long Answer Type Question Answer**

1. (i) From Snell’s law, μ = sin i / sin r = c / v

v ∝ sin r

Smaller the angle of refraction, smaller the velocity of light in medium.

Velocity of light is minimum in medium A, as the angle of refraction is minimum, i.e. 15^{o}.

(ii) Whenever rays of light travels through glass, they strike the glass-air interface at an angle greater than critical angle of glass. They are totally reflected, hence cracks appear silvery.

(iii) The refractive index of diamond is much higher than that of glass. Due to high refractive index, the critical angle for diamond-air interface is low. The diamond is cut suitably, so that the light entering the diamond from any face suffers multiple total internal reflections at the various surfaces. This gives sparkling effect to the diamonds.

(iv) Here, μ = thickness of object / apparent depth

Now due to refraction at 2 different boundaries, the apparent depth of object

= (thickness of glass/μ_{glass}) + (thickness of water/μ_{water})

= (6/1.5) + (4/1.3)

= 4 + 3 = 7

**Final Words**

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