A ray of light incident normally on an isosceles right angled prism travels as shown in the figure. The least value of the refractive index of the prism must be

Question

A ray of light incident normally on an isosceles right angled prism travels as shown in the figure. The least value of the refractive index of the prism must be (A) √2 (B) √3 (C) 1.5 (D) 2.0

Tardigrade Admin · Accepted Answer

From figure it is clear that TIR takes place at surface

A C

and

BC

i.e.,

4 5^{\circ} > C

\Rightarrow sin 4 5^{\circ} > sin C

\Rightarrow \frac{1}{2} > \frac{1}{μ} \Rightarrow μ > 2

\Rightarrow μ > 2

Hence

μ_{least} = 2

Q. A ray of light incident normally on an isosceles right angled prism travels as shown in the figure. The least value of the refractive index of the prism must be

$2$

$3$

$1.5$

$2.0$

From figure it is clear that TIR takes place at surface $A C$ and $BC$
i.e., $4 5^{\circ} > C$

$\Rightarrow sin 4 5^{\circ} > sin C$
$\Rightarrow \frac{1}{2} > \frac{1}{μ} \Rightarrow μ > 2$
$\Rightarrow μ > 2$
Hence $μ_{least} = 2$

Q. A ray of light incident normally on an isosceles right angled prism travels as shown in the figure. The least value of the refractive index of the prism must be

2​

3​

1.5

2.0

From figure it is clear that TIR takes place at surface AC and BC i.e., 45∘>C ⇒sin45∘>sinC ⇒2​1​>μ1​⇒μ>2​ ⇒μ>2​ Hence μleast ​=2​

$2$

$3$

$1.5$

$2.0$

From figure it is clear that TIR takes place at surface $A C$ and $BC$
i.e., $4 5^{\circ} > C$

$\Rightarrow sin 4 5^{\circ} > sin C$
$\Rightarrow \frac{1}{2} > \frac{1}{μ} \Rightarrow μ > 2$
$\Rightarrow μ > 2$
Hence $μ_{least} = 2$