Q20
jee_main_2025_03_april_morning
Minimum Deviation in Prism
Consider following statements for refraction of light through prism, when angle of deviation is minimum.
(A) The refracted ray inside prism becomes parallel to the base.
(B) Larger angle prisms provide smaller angle of minimum deviation.
(C) Angle of incidence and angle of emergence becomes equal.
(D) There are always two sets of angle of incidence for which deviation will be same except at minimum deviation setting.
(E) Angle of refraction becomes double of prism angle.
Choose the correct answer from the options given below.
Solution
### Related Formula
For a prism of angle A:
- Deviation: delta = i + e - A
- Minimum deviation delta_textmin occurs when:
i = e quad textand quad r_1 = r_2 = fracA2
- Under minimum deviation, the ray inside an equilateral/isosceles prism travels symmetrically, making it parallel to the prism base.
### Core Logic
Let's check the validity of each statement:
- **Statement (A)**: The refracted ray inside the prism becomes parallel to the base at minimum deviation. (True for symmetric prisms)
- **Statement (B)**: Larger angle prisms provide smaller minimum deviation. By minimum deviation equation:
mu = fracsinleft(fracA+delta_textmin2right)sinleft(fracA2right)
As A increases, delta_textmin generally increases, not decreases. (False)
- **Statement (C)**: Angle of incidence i and angle of emergence e become equal (i = e) during the minimum deviation state. (True)
- **Statement (D)**: The delta-i curve is asymmetric and parabolic-like; for any deviation delta > delta_textmin, there are always exactly two different incident angles (i and e) that yield the same deviation, except at the minimum deviation point (which has a single unique value). (True)
- **Statement (E)**: Angle of refraction r = A/2, which is half of the prism angle, not double. (False)
### Step 1: Conclusion
Since statements A, C, and D are true, the correct option is (1).
### Pattern Recognition
Review the classic parabolic shape of the deviation vs. angle of incidence (delta-i) graph. Notice that any horizontal line above the minimum point intersects twice (representing i and e for that deviation). Minimum deviation is the unique local minimum, where i = e and r_1 = r_2 = A/2.
### Evaluation Rubric / Model Answer
null
### Chapter Mix
Class 12 Physics: Ray Optics and Optical Instruments: Refraction through Prism
