Question

A thin prism p1 with angle 4 and made from glass (=1.54) is combined with another prism p2 made of another glass of =1.72 to produce dispersion without deviation. The angle of prism p2 is

Answer 1

Explanation:

For a thin prism, angle of minimum deviation is given by

δ=(μ−1)A

where,μ is refractive index of the prism and A the angle of prism.

For dispersion without deviation

δ1=δ2

⇒(μ1−1)A1=(μ2−1)A2

⇒A2=(μ1−1)(μ2−1)A1

Given, μ1=1.54,A1=4∘,μ2=1.72

⇒A2=(1.54−1)(1.72−1)×4=3∘

Answer 2

The angle of prism P₂ is 3°.

Explanation:

Given that,

Angle = 4°

Refractive index of the prism P₁= 1.54

Refractive index of the prism P₂= 1.72

We need to calculate the angle of prism P₂

Using formula of deviation

$\delta=(\mu-1)A$

For prism P₁,

$\delta_{1}=(\mu-1)4$

For prism P₂,

$\delta_{2}=(\mu-1)A$

For no deviation,

$\delta_{1}=\delta_{2}$

Put the value into the formula

$(\mu-1)4=(\mu-1)A$

$A=\dfrac{(1.54-1)4}{(1.72-1)}$

$A=3^{\circ}$

Hence, The angle of prism P₂ is 3°.

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Topic : deviation

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