A planar structure of length L and width W is | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) For the maximum time,the ray of light must undergo $TIR$ at all surfaces at the minimum possible angle,which is the critical angle $	heta_c$.For

Vedclass · Accepted Answer

$50$

Vedclass · Answer

(B) For the maximum time,the ray of light must undergo $TIR$ at all surfaces at the minimum possible angle,which is the critical angle $	heta_c$.For $TIR$,the condition is $n_1 \sin 	heta_c = n_2$.$\sin 	heta_c = \frac{n_2}{n_1} = \frac{1.44}{1.5} = 0.96$.The speed of light in the medium $n_1$ is $v = \frac{c}{n_1} = \frac{3 	imes 10^8}{1.5} = 2 	imes 10^8 \ m/s$.Let the total path length of the ray inside the structure be $D$. The horizontal length is $L$. The angle the ray makes with the normal to the surface is $	heta_c$. Therefore,the horizontal component of the path is $D \sin 	heta_c = L$.Thus,$D = \frac{L}{\sin 	heta_c}$.The time taken is $t_{total} = \frac{D}{v} = \frac{L}{v \sin 	heta_c} = \frac{9.6}{(2 	imes 10^8) 	imes 0.96} = \frac{9.6}{1.92 	imes 10^8} = 5 	imes 10^{-8} \ s = 50 	imes 10^{-9} \ s$.Therefore,$t = 50$.

Similar Questions

What should be the maximum acceptance angle at the air-core interface of an optical fibre if $n_1$ and $n_2$ are the refractive indices of the core and the cladding respectively?

In an optical fibre, the core and cladding are made with materials of refractive indices $1.5$ and $1.414$ respectively. To observe total internal reflection, what will be the range of the incident angle with the axis of the optical fibre?

$A$ ray of light travels from an optically denser medium to a rarer medium. The critical angle for the two media is $C$. The maximum possible deviation of the refracted light ray can be:

$A$ small coin is resting on the bottom of a beaker filled with liquid. $A$ ray of light from the coin travels up to the surface of the liquid and moves along its surface. How fast is the light travelling in the liquid?

Vedclass Test Series

Exam Paper Generator

Online Exam Module