The angle of incidence for a ray of light at a refracting surface of a prism is 45°. The angle of prism is 60° . If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are :

Question

The angle of incidence for a ray of light at a refracting surface of a prism is 45°. The angle of prism is 60° . If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are : (A) 30° ; √2 (B) 45° ; √2 (C) 30° ; (1/ √2) (D) 45° ; (1/ √2)

Tardigrade Admin · Accepted Answer

i = 45° ; A = 60° ; δm = 2i - A = 30° μ = ( sin((A + δm/2))/ sin A/2) = ( sin45°/ sin30°) = (1/√2). (2/1) = √2

Q. The angle of incidence for a ray of light at a refracting surface of a prism is $4 5^{\circ}$ . The angle of prism is $6 0^{\circ}$ . If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are :

$3 0^{\circ}; 2$

$4 5^{\circ}; 2$

$3 0^{\circ}; \frac{1}{2}$

$4 5^{\circ}; \frac{1}{2}$

$i = 4 5^{\circ}; A = 6 0^{\circ}; δ_{m} = 2 i - A = 3 0^{\circ}$
$μ = \frac{s i n ( \frac{A + δ _{m}}{2} )}{s i n A /2} = \frac{s i n 4 5 ^{\circ}}{s i n 3 0 ^{\circ}} = \frac{1}{2} . \frac{2}{1} = 2$

Q. The angle of incidence for a ray of light at a refracting surface of a prism is 45∘. The angle of prism is 60∘. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are :

30∘;2​

45∘;2​

30∘;2​1​

45∘;2​1​