Lumos

Question:

A photon starts moving in the random direction from the center of the square of size 3. Let’s say it first colloids to the glass wall AB. What is the expected distance traveled by the photon before hitting the wall AB again?

.

.

C

A

P

T

A

I

N

I

N

T

E

R

V

I

E

W

.

.

Solution:

final22-300x212.jpg

Above is a pictorial representation of the photon. We can calculate it’s distance as shown below:

d= x cosec (Θ)

d= (3 - x) cosec (Θ)

d= (3 - y) cosec (Θ)

d= y cosec (Θ)

Total distance = d1+ d2 + d3 + d4

6 cosec (Θ)

We know, Θ varies between Π/4 and 3Π/4

Therefore, E(distance) = 6 E (cosec Θ)
6 x (2 /Π) ∫cosec(Θ)dΘ    (limits Π/4 to 3Π/4)
12/Π ln (√2 + 1/√2 + 1

 

 

 

 

 

 

 

 

 

 

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

w

Connecting to %s