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प्रश्न
With the help of a ray diagram, state what is meant by refraction of light. State Snell’s law for refraction of light and also express it mathematically.
The refractive index of air with respect to glass is 2/3 and the refractive index of water with respect to air is 4/3. If the speed of light in glass is 2 × 108 m/s, find the speed of light in (a) air, (b) water.
उत्तर
When a ray of light travels from one transparent medium to another, it bends at the surface. This happens because different media have different optical densities.
The phenomenon of bending of light as it travels from one medium to another is known as refraction of light.
As a ray of light moves from an optically rarer medium to an optically denser medium, it bends towards the normal at the point of incidence. Therefore, the angle of incidence (i) is greater than the angle of refraction (r). Hence, i > r
The first law of refraction is also known as Snell’s law.
Snell’s law: The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant. This is known as Snell’s law. Mathematically, it can be given as follows:
`sini/sinr="constant"=`\[^aμ_b\]
\[^gμ_a\] `=2/3=μ_a/μ_g`
\[^aμ_w\]`=4/3=μ_w/μ_a`
Vg = 2 × 108 m/s
Now we know μ=`C/V`
Where µ is absolute refractive index of a medium w.r.t. vacuum
C is speed of light in vacuum
V is speed of light in medium.
(a) Now `μ_a=C/V`
`μ_g=C/V_g`
Dividing `μ_a/μ_g=V_g/V_a=2/3`
`V_a=3/2xxV_g=3/2xx2xx10^8` m/s
`=3xx10^8`m/s
(b) Again `μ_w=C/V_w`
`μ_a=C/V_a`
Dividing `μ_w/μ_a=V_a/V_w=4/3`
`V_w=3/4xx3xx10^8`
`=9/4xx10^8`
= 2.25 x 108 m/s
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संबंधित प्रश्न
The refractive indices of glass and water with respect to air are 3/2 and 4/3 respectively. If speed of light in glass is 2 x 108 m/s, find the speed of light in water.
The absolute refractive indices of two media 'A' and 'B' are 2.0 and 1.5 respectively. If the speed of light in medium 'B' is 2 × 108 m/s, calculate the speed of light in:
(i) vacuum,
(ii) medium 'A'.
A ray of light travelling in water falls at right angles to the boundary of a parallel-sided glass block. The ray of light:
(a) is refracted towards the normal
(b) is refracted away from the normal
(c) does not get refracted
(d) is reflected along the same path
The refractive index of glass for light going from air to glass is The refractive index for light going from glass to air will be:
(a) `1/3`
(b) `4/5`
(c) `4/6`
(d) `5/2`
The speed of light in substance X is 1.25 × 108 m/s and that in air is 3 × 108 m/s. The refractive index of this substance will be:
(a) 2.4
(b) 0.4
(c) 4.2
(d) 3.75
The refractive index of glass with respect to air is `3/2` and the refractive index of water with respect to air is `4/3`. The refractive index of glass with respect to water will be:
(a) 1.525
(b) 1.225
(c) 1.425
(d) 1.125
The following table gives the refractive indices of a few media:
| 1 | 2 | 3 | 4 | 5 | |
| Medium | Water | Crown glass | Rock salt | Ruby | Diamond |
| Refractive index | 1.33 | 1.52 | 1.54 | 1.71 | 2.42 |
Use this table to give an example of:
(i) a medium pair so that light speeds up when it goes from one of these medium to another.
(ii) a medium pair so that light slows down when it goes from one of these medium to another.
n = _______. This law is also called as Snell’s law.
Refractive index of diamond with respect to glass is 1.6 and absolute refractive index of glass is 1.5. Find out the absolute refractive index of diamond.
How is the refractive index of material related to the velocity of light?
