CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Use Huygens' Principle to show how a plane wave front propagates from a denser to rarer medium. Hence, verify Snell's law of refraction.


Solution

We assume a plane wave front AB propagating in denser medium incident on the interface PP at angle i as shown in 
Fig. 
Let T be the time taken by the wave front to travel a distance BC. If vi is the speed of the light in medium I.
So, $$BC = v_1 T$$ 

In order to find the shape of the refracted wave front, we draw a sphere of radius $$AE = v_2 T$$ , where $$v_2$$ is the speed of light in medium II (rarer medium). 
The tangent plane CE represents the refracted wave front 
In $$\Delta ABC = sin \ i = \frac{BC}{AC} = \frac{v_1t}{AC}$$
and in $$\Delta ACE = sin \ r = \frac{AE}{AC} = \frac{v_2t}{AC}$$
$$\therefore \ \ \frac{sin \ i}{sin \ r} \frac{BC}{AE} = \frac{v_1t}{v_2t} = \frac{v_1}{v_2}$$       ...(1)
Let c be the speed of light in vacuum 
So, $$\mu_1 = \frac{C}{v_1}$$ and $$ \mu_2 = \frac{C}{v_2}$$
$$\frac{\mu_2}{\mu_1} = \frac{v_1}{v_2}$$                                                                            ...(2)
From equations (1) and (2), we have
$$\frac{sin \ i}{sin \ r} = \frac{\mu_2}{\mu_1}$$
$$\mu_1 \ sin \ i = \mu_2 \ sin \ r$$
It is known as Snell's law.

1654768_1784583_ans_c5d5b9b062c343e0ab33e6f1cc64e9d5.png

Physics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image