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प्रश्न
| The ability of medium to refract light is expressed in terms of its optical density. Optical density has a definite connotation. It is not the same as mass density. On comparing two media, the one with the large refractive index is optically denser medium than the other. The other medium with a lower refractive index is optically rarer. Also the speed of light through a given medium is inversely proportional to its optical density. |
- Determine the speed of light in diamond if the refractive index of diamond with respect to vacuum is 2.42. Speed of light in vacuum is 3 × 108 m/s.
- Refractive indices of glass, water and carbon disulphide are 1.5, 1.33 and 1.62 respectively. If a ray of light is incident in these media at the same angle (say θ), then write the increasing order of the angle of refraction in these media.
- (A) The speed of light in glass is 2 × 108 m/s and is water is 2.25 × 108 m/s.
(a) Which one of the two optically denser and why?
(b) A ray of light is incident normally at the water glass interface when it enters a thick glass container filled with water. What will happen to the path of the ray after entering the glass? Give reason.
OR
(B) The absolute refractive indices of glass and water are 4/3 and 3/2, respectively. If the speed of light in glass is 2 × 108 m/s, calculate the speed of light in (i) vacuum (ii) water.
उत्तर
(i) Refractive index of diamond,
n = `"Speed of light in vacuum"/"Speed of light in diamond"`
n = `"c"/"v"`
2.42 = `(3xx10^8)/"Speed of light in diamond"`
Speed of light in diamond = `(3xx10^8)/2.42`
= 1.25 × 108 m/s.
(ii) rwater < rglass < `"r"_"carbon disulphide"`
(iii) (A) (a) Since the speed of light is greater in water than in glass, glass is optically denser than water. This demonstrates that glass presents a greater barrier to light transmission than water.
(b) After refraction, the light will bend towards normal.
OR
(B) Refractive index of glass, ηg = 4/3
`thereforeeta_g="Speed of light in vacuum"/"Speed of light in glass"`
`4/3="Speed of light in vacuum"/(2xx10^8)`
`"Speed of light in vacuum "=(4xx2xx10^8)/3=2.6xx10^8"m/s"`
`"Refractive index of water,"eta_w=3/2`
`eta_w="Speed of light in vacuum"/"Speed of light in water"`
`3/2=(2.6xx10^8)/"Speed of light in water"`
`"Speed of light in water" = 1.73 xx 10^8 "m/s"`
Because the information provided is wrong, ideally the speed of light in vacuum is 3 × 108 m/s and the speed of light in water is 2.25 × 108 m/s.
The correct solution is
`"Refractive index of glass,"eta_g=3/2`
`"Refractive index of water,"eta_w=4/3`
`"Refractive index of glass,"eta_g="Speed of light in vacuum"/"Speed of light in glass"`
`3/2="Speed of light in vacuum"/(2xx10^8)`
`"Speed of light in vacuum "=(3xx2xx10^8)/2=3xx10^8"m/s"`
`"Refractive index of water, "eta_w=4/3`
`eta_w="Speed of light in vacuum"/"Speed of light in water"`
`4/3=(3xx10^8)/"Speed of light in water"`
`"Speed of light in water "=(3xx3xx10^8)/4`
`"Speed of light in water "=2.25xx10^8"m/s"`
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संबंधित प्रश्न
Give three examples of materials that refract light rays. What happens to the speed of light rays when they enter these materials?
The speed of light in vacuum and in two different glasses is given in the table below:
| Medium | Speed of light |
| Vacuum | 3.00 × 108 m/s |
| Flint glass | 1.86 × 108 m/s |
| Crown glass | 1.97 × 108 m/s |
(a) Calculate the absolute refractive indexes of flint glass and crown glass.
(b) Calculate the relative refractive index for light going from crown glass to flint glass.
Light enters from air into diamond which has a refractive index of 2.42. Calculate the speed of light in diamond. The speed of light in air is 3.0 × 108 ms−1.
The refractive indices of four substance P, Q, R and S are 1.50, 1.36, 1.77 and 1.31 respectively. The speed of light is the maximum in the substance:
(a) P
(b) Q
(c) R
(d) S
State the laws of refraction of light. Explain the term 'absolute refractive index of a medium' and write an expression to relate it with the speed of light in vacuum.
The refractive indices of water and glass with respect to air are 4/3 and 3/2 respectively. If the speed of light in glass is 2 × 108ms−1, find the speed of light in (i) air, (ii) water.
State Snell’s law of refraction of light. Write an expression to relate refractive index of a medium with speed of light in vacuum.
The refractive index of a medium ‘a’ with respect to medium ‘b’ is 2/3 and the refractive index of medium ‘b’ with respect to medium ‘c’ is 4/3. Find the refractive index of medium ‘c’ with respect to medium ‘a’.
Prove the statement.
If the angle of incidence and angle of emergence of a light ray falling on a glass slab are i and e respectively, prove that, i = e.
_______ is the unit of refractive index.
Absolute refractive indices of diamond and water are 2.42 and 1.33 respectively. Find the value of refractive index of water w.r.t. diamond.
