Related Problems with Solution

Problem 1 : Reflection and Refraction

Problem Statement: A beam of light traveling in air n1=1 enters a glass block n2=1.5 at an angle of incidence (i) of (30). Calculate the angle of refraction (r) inside the glass block and determine whether total internal reflection occurs at the glass-air interface.

Solution :
  • Step 1: Use Snell’s Law to find the angle of refraction ((r)):(n1sin(i)=n2sin(r)).
  • Step 2: Substitute values: (1sin(30)=1.5sin(r)).
  • Step 3: Solve for (r):(r=sin1(11.5sin(30))).

The angle of refraction ((r)) can be calculated, and it turns out to be (20^\circ). Now, let’s check if total internal reflection occurs:

  • Total Internal Reflection Condition: (i>θc), where θc is the critical angle.
  • Calculate the critical angle: (θc=sin1(n2n1)).
  • Substitute values: (θc=sin1(1.51)).

Since the angle of incidence ((i=30)) is greater than the critical angle ((θc48.59)), total internal reflection does not occur.