Numerical Problems Based on Refraction of Light for Class 12 Physics

Numerical Problems Based on Refraction of Light for Class 12 Physics

Here we are providing numerical problems based on refraction of light for class 12 physics. This covers problems on lateral shift, real and apparent depth. Students can practice these questions for better understanding of the concepts and formulae.

Q.1. A ray of light of frequency 5 × 10¹⁴ Hz is passed through a liquid. The wavelength of light measured inside the liquid is found to be 450 x 10^-9 m. Calculate the refractive index of the liquid.

Q.2. A ray of light passes through a plane boundary separating two media whose refractive indices are μ₁ =3/2 and μ₂ =4/3. (i) If the ray travels from medium 1 to medium 2 at an angle of incidence of 30°, what is the angle of refraction? (ii) If the ray travels from medium 2 to medium 1 at the same angle of incidence, what is the angle of refraction?

Q.3. A cylindrical vessel of diameter 12 cm contains 800 π on³ of water. A cylindrical glass piece of diameter 8.0 cm and height 8.0 cm is placed in the vessel. If the bottom of the vessel under the glass piece is seen by the paraxial rays (see figure), locate its image. The index of refraction of glass is 1.50 and that of water is 1.33.

Q.4. The bottom of a container is a 4.0 cm thick glass (μ =1.5) slab. The container contains two immiscible liquids A and B of depths 6.0 cm and 8.0 cm respectively. What is the apparent position of a scratch on the outer surface of the bottom of the glass slab when viewed through the container? Refractive indices of A and B are 1.4 and 1.3 respectively.

Q.5. The velocity of light in glass is 2 × 10⁸ms^-1 and that in air is 3×10⁸ ms^-1. By how much would an ink dot appear to be raised, when covered by a glass plate 6.0 cm thick?

Q.6. A light of wavelength 6000  in air, enters a medium with refractive index 1.5. What will be the frequency and wavelength of light in that medium?

Q.7. A rectangular glass slab rests in the bottom of a trough of water. A ray of light incident on water surface at an angle of 50° passes through water into glass. Calculate the angle of refraction in glass. Given that μ for water is 4/3 and that for glass is 3/2.

Q.8. The apparent depth of an object at the bottom of tank filled with a liquid of refractive index 1.3 is 7.7 cm. What is the actual depth of the liquid in the tank?

Q.9. A mark is made on the bottom of a beaker and a microscope is focussed on it. The microscope is raised through 1.5 cm. To what height water must be poured into the beaker to bring the mark again into focus? Given that μ for water is 4/3.

Q.10. A printed page is kept pressed by a glass cube (μ = 1.5) of edge 6.0 cm. By what amount will the printed letters appear to be shifted when viewed from the top?

Q.11. The velocity of light in a transparent medium is 1.8 x10⁸ms^-1, while that in vacuum is 3 x10⁸ms^-1. Find by how much the bottom of the vessel containing the liquid appears to be raised if the depth of the liquid is 0.25 m.

Q.12. A vessel contains water upto a height of 20 cm and above it an oil upto another 20 cm. The refractive indices of water and oil are 1.33 and 1.30 respectively. Find the apparent depth of vessel when viewed from above.

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