Question

if the minimum deviation produced by glass prism of angle 60 to 30 degree find the speed of light in glass ​

Answer 1

Answer:

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n = Sin[(60°+30°)/2]/Sin 60°/2 = Sin 45°/Sin 30° = [(1/√2)/(1/2)]= 2/√2 = √2. Velocity of light in glass= ( velocity of light in vaccum)/n = 3×10^8 m/s / √2= 2.12×10^8 m/s.

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Answer 2

The speed of light in glass is $2.1\times10^{8}\ m/s$

Explanation:

Given that,

Angle of prism A= 60°C

Minimum deviation = 30°C

Let, The refractive index of air = n₁

Refractive index of glass = n₂

We need to calculate the refractive index of glass with respect to air

Using formula of refractive index

$\dfrac{n_{2}}{n_{1}}=\dfrac{\sin(\dfrac{A+D_{m}}{2})}{\sin(\dfrac{A}{2})}$

Put the value into the formula

$\dfrac{n_{2}}{n_{1}}=\dfrac{\sin(\dfrac{60+30}{2})}{\sin(\dfrac{60}{2})}$

$\dfrac{n_{2}}{n_{1}}=1.41$

We need to calculate the speed of light in glass

Using formula of speed of light in glass

$v_{2}=\dfrac{v}{\dfrac{n_{2}}{n_{1}}}$

$v_{2}=\dfrac{3\times10^{8}}{1.41}$

$v_{2}=2.1\times10^{8}\ m/s$

Hence, The speed of light in glass is $2.1\times10^{8}\ m/s$

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Topic : refractive index

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