Question

A thin prism of refracting angle 8 degree produces a deviation of 4 degree. The refractive index of
the material of the prism is
(A) 1.33
(B) 1.5
(C) 0.5
(D) 1.25​

Answer 1

Given angle of prism=

5 0

and angle of deviation δm=

1.5 0

Refractive index of the material

μ=

sin

2

A

2

sinA+δm

=

sin(

2

5

)

sin

2

(5+1.5)

=

0.04361

0.0567

Answer 2

Answer:

The refractive index of the material of the prism is 1.5 i.e.option(B)

Explanation:

For a small angled prism(A less than or equal to 10°) the relation between prism angle, deviation and refractive index is given by;

$\delta=A(\mu-1)$         (1)

where,

δ=deviation in the prism

A=prism angle

μ=refractive index of the prism

The values given in the question are,

δ=4°

A=8°

By putting the value of δ and A in equation (1) we get;

$4=8(\mu-1)$

$\mu-1=0.5$

$\mu=1.5$

Hence, the refractive index of the material of the prism is 1.5 i.e.option(B)