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Question
CBSEENSC10014826

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 x 10m/s, find the speed of light in:
a) air, b) water.

Solution

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.
refraction of light is the phenomenon of bending of light as it travels from one medium to another is known as refraction of light.
When a ray of light moves from optically rarer medium to an optically denser medium, it bends towards the normal at the point of incidence.
Therefore, angle of incidence (i) is greater than the angle of refraction (r).

Snell's law states that, the ratio of the angle of incidence to the sine of the angle of refraction is constant.
Mathematically, it is given as,
fraction numerator sin space straight i over denominator sin space straight r end fraction space equals space c o n s tan t space equals space mu presuperscript a subscript b

H e r e comma

mu presuperscript g subscript a space equals space 2 over 3 equals mu subscript a over mu subscript g
mu presuperscript a subscript w space equals space 4 over 3 equals mu subscript w over mu subscript a
v subscript g space equals space 2 space x space 10 to the power of 8 space m divided by s

A l s
mu space equals space c over v
where, straight mu is the absolute refractive index of a medium w.r.t vacuum
c is the speed of light in vacuum
v is the speed of light in medium
a) Now,
straight mu subscript straight a space equals space straight c over straight v subscript straight a
straight mu subscript straight g space equals space straight c over straight v subscript straight g
Dividing space straight mu subscript straight a over straight mu subscript straight g equals straight V subscript straight g over straight V subscript straight a equals 2 over 3
straight V subscript straight a space equals space 3 over 2 xV subscript straight g space
space space space space space equals space 3 over 2 straight x 2 straight x 10 to the power of 8 space straight m divided by straight s
space space space space space equals space 3 space straight x space 10 to the power of 8 space straight m divided by straight s
b) We have,
straight mu subscript straight w space equals space straight c over straight V subscript straight w
straight mu subscript straight a space equals space straight C over straight V subscript straight a
Dividing space straight mu subscript straight w over straight mu subscript straight a equals straight v subscript straight a over straight v subscript straight w equals 4 over 3
straight v subscript straight w space equals space 3 over 4 straight x 3 space straight x space 10 to the power of 8
space space space space space equals space 9 over 4 straight x space 10 to the power of 8
space space space space space space equals space 2.25 space straight x space 10 to the power of 8 space straight m divided by straight s