Question
Hard
Solving time: 4 mins
A right angled prism is to be made by selecting a proper material and the angles and , as shown in figure. It is desired that a ray of light incident on the face emerges parallel to the incident direction after two internal reflections.
(a) What should be the minimum refractive index for this to be possible?
(b) For is it possible to achieve this with the angle equal to 30 degrees?
Text solutionVerified
(a) At , angle of incidence and at , angle of incidence
If conditin of TIR is satisfied for the smaller a incidence than for larger angle of incidence it automatically satisfied.
Let us take and , then to satis condition of TIR on both points and .
Now, let us take and . Then
So, as in increasing desired value of is decreasing.
Maximum value of for the condition is .
For that .
(b)
i.e. TIR will take place at but not at .
or we write :
or
If conditin of TIR is satisfied for the smaller a incidence than for larger angle of incidence it automatically satisfied.
Let us take and , then to satis condition of TIR on both points and .
Now, let us take and . Then
So, as in increasing desired value of is decreasing.
Maximum value of for the condition is .
For that .
(b)
i.e. TIR will take place at but not at .
or we write :
or
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Question Text | A right angled prism is to be made by selecting a proper material and the angles and , as shown in figure. It is desired that a ray of light incident on the face emerges parallel to the incident direction after two internal reflections. (a) What should be the minimum refractive index for this to be possible? (b) For is it possible to achieve this with the angle equal to 30 degrees? |
Updated On | Oct 25, 2022 |
Topic | Ray Optics and Optical Instruments |
Subject | Physics |
Class | Class 12 |
Answer Type | Text solution:1 Video solution: 6 |
Upvotes | 732 |
Avg. Video Duration | 8 min |