Practise: Refractive Index - Vardaan Learning Institute

1. The refractive index ($n$) of a medium is defined as:
(a) Speed of light in medium / Speed of light in vacuum
(b) Speed of light in vacuum / Speed of light in medium
(c) Speed of light in medium $\times$ Speed of light in vacuum
(d) None of the above

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2. Which of the following statements is true for a ray of light entering from air into water?
(a) Values of speed and frequency change.
(b) Values of speed and wavelength change.
(c) Values of wavelength and frequency change.
(d) Values of speed, wavelength, and frequency change.

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3. The refractive index of water is 1.33 and that of glass is 1.50. The refractive index of glass with respect to water is:
(a) $1.33 / 1.50$
(b) $1.50 / 1.33$
(c) $1.50 \times 1.33$
(d) $1.50 - 1.33$

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4. Absolute refractive index of any medium is always:
(a) Less than 1
(b) Equal to 1
(c) Greater than 1
(d) Zero

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5. If the speed of light in a medium is $2 \times 10^8$ m/s, its refractive index is:
(a) 1.0
(b) 1.5
(c) 0.5
(d) 2.0

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6. When light travels from a denser medium to a rarer medium, it bends:
(a) Towards the normal
(b) Away from the normal
(c) Along the normal
(d) Does not bend

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7. Optical density is different from mass density. Kerosene having higher refractive index than water is:
(a) Optically rarer than water
(b) Optically denser than water
(c) Has same optical density
(d) None of these

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8. The unit of refractive index is:
(a) m/s
(b) Diopter
(c) Degree
(d) No unit

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9. Which color of white light deviates the most when passing through a glass prism?
(a) Red
(b) Violet
(c) Green
(d) Yellow

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10. According to Snell's Law:
(a) $i = r$
(b) $\sin i / \sin r = \text{constant}$
(c) $\sin r / \sin i = \text{constant}$
(d) $i + r = 90^{\circ}$

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11. Assertion (A): The refractive index of diamond is very high (2.42).
Reason (R): The speed of light in diamond is very low compared to vacuum.
(a) Both A and R are true and R is correct explanation of A.
(b) Both A and R are true but R is NOT correct explanation.
(c) A is true, R is false.
(d) A is false, R is true.

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12. Assertion (A): A ray of light passing from air to glass bends towards the normal.
Reason (R): Light travels faster in glass than in air.
(a) Both A and R are true and R is correct explanation of A.
(b) Both A and R are true but R is NOT correct explanation.
(c) A is true, R is false.
(d) A is false, R is true.

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13. Assertion (A): Refractive index has no units.
Reason (R): It is a ratio of two similar physical quantities (speeds).

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14. Light enters from air to glass having refractive index 1.50. What is the speed of light in glass? (Speed of light in vacuum is $3 \times 10^8$ m/s).

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15. The refractive index of medium A is 1.5 and that of medium B is 1.33. In which medium does light travel faster? Justify your answer.

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16. Calculate the refractive index of a medium if the speed of light in that medium is $2.25 \times 10^8$ m/s.

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17. State the laws of refraction of light. Define the constant introduced in the second law.

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18. Why does a pencil partly immersed in water appear to be bent at the water surface? Draw a ray diagram to support your answer.

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19. Refractive indices of alcohol and turpentine oil are 1.36 and 1.47 respectively. Find the refractive index of turpentine oil with respect to alcohol.

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20. A coin kept at the bottom of a glass bowl filled with water appears raised. Explain this phenomenon with a diagram.

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21. If the refractive index of water w.r.t air is $4/3$ and glass w.r.t air is $3/2$, find the refractive index of glass w.r.t water.

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22. Define 'Optical Density'. How is it different from mass density? Give an example where a medium with higher mass density has lower optical density.

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23. A ray of light travels from Medium 1 to Medium 2. The angle of incidence is $45^\circ$ and the angle of refraction is $30^\circ$. Calculate the refractive index of Medium 2 with respect to Medium 1. (Given $\sin 45^\circ = 0.707, \sin 30^\circ = 0.5$).

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24. (a) Define absolute refractive index.
(b) The speed of light in a transparent medium is 0.6 times that of its speed in vacuum. What is the refractive index of the medium?
(c) Why does a ray of light bend when it travels from one medium to another?

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25. Case Study: A student performs an experiment with a glass slab to trace the path of a light ray.
(i) What is lateral displacement?
(ii) On what factors does lateral displacement depend?
(iii) If the refractive index of the slab increases, how does lateral displacement change?

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26. (a) Prove that if a ray enters from air to water and then to glass, the product of refractive indices: $_a n_w \times _w n_g \times _g n_a = 1$.
(b) Find the critical angle definition in terms of refractive index.

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28. Atmospheric Refraction:
(a) Why do stars twinkle but planets do not?
(b) Why does the sun appear visible 2 minutes before actual sunrise?
Explain solely based on the concept of changing refractive index of layers of air.

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29. A ray of light enters a rectangular glass slab of refractive index 1.5. The angle of incidence is $60^\circ$.
(i) Use Snell's Law to calculate the angle of refraction (Given $\sin 60 = 0.866$).
(ii) Show that the emergent ray is parallel to the incident ray.

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30. Conceptual Analysis:
Three media A, B, and C have refractive indices 1.3, 1.5, and 2.0 respectively.
(i) In which medium is the speed of light maximum?
(ii) In which medium is the speed of light minimum?
(iii) If light travels from A to B, does it bend towards or away from normal?
(iv) If light travels from C to B, does it bend towards or away from normal?

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