Question:
The refractive index of a prism with apex angle \( A \) is \( \cot \frac{A}{2} \). The angle of minimum deviation is:
The refractive index of a prism with apex angle \( A \) is \( \cot \frac{A}{2} \). The angle of minimum deviation is:
Updated On: Nov 20, 2024
- \( \delta_m = 180^\circ - A \)
- \( \delta_m = 180^\circ - 3A \)
- \( \delta_m = 180^\circ - 4A \)
- \( \delta_m = 180^\circ - 2A \)
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
Given:
\[ \mu = \frac{\sin \left( \frac{A + \delta_m}{2} \right)}{\sin \frac{A}{2}} \]
Using the relation:
\[ \cos \frac{A}{2} = \sin \left( \frac{A + \delta_m}{2} \right) \]
We get:
\[ \delta_m = \pi - 2A \]
Therefore:
\[ \delta_m = 180^\circ - 2A \]
Was this answer helpful?
0
0
Top Questions on Optics
- Name the type of lenses required by the persons for the correction of their defect of vision called presbyopia. Write the structure of the lenses commonly used for the correction of this defect giving reason for such designs.
- A beam of light coming from a distant source is refracted by a spherical glass ball (refractive index 1.5) of radius 15 cm. Draw the ray diagram and obtain the position of the final image formed.
- A double convex lens of glass has both faces of the same radius of curvature 17 cm. Find its focal length if it is immersed in water. The refractive indices of glass and water are 1.5 and 1.33 respectively.
- A point source is placed at the bottom of a tank containing a transparent liquid (refractive index \( n \)) to a depth H. The area of the surface of the liquid through which light from the source can emerge out is:
- Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : If Young’s double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer.
Reason (R) : The speed of light reduces in an optically denser medium than air while its frequency does not change.
In the light of the above statements, choose the most appropriate answer from the options given below :
View More Questions
Questions Asked in JEE Main exam
- If \( \alpha + i\beta \) and \( \gamma + i\delta \) are the roots of the equation \( x^2 - (3-2i)x - (2i-2) = 0 \), \( i = \sqrt{-1} \), then \( \alpha\gamma + \beta\delta \) is equal to:
- JEE Main - 2025
- Complex numbers
- If \( \alpha \) and \( \beta \) are the roots of the equation \( 2z^2 - 3z - 2i = 0 \), where \( i = \sqrt{-1} \), then \[ 16 \cdot {Re} \left( \frac{\alpha^{19} + \beta^{19} + \alpha^{11} + \beta^{11}}{\alpha^{15} + \beta^{15}} \right) \cdot {Im} \left( \frac{\alpha^{19} + \beta^{19} + \alpha^{11} + \beta^{11}}{\alpha^{15} + \beta^{15}} \right) \] is equal to:
- JEE Main - 2025
- Complex numbers
Statement-1: \( \text{ClF}_3 \) has 3 possible structures.
Statement-2: \( \text{III} \) is the most stable structure due to least lone pair-bond pair (lp-bp) repulsion.
Which of the following options is correct?
- JEE Main - 2025
- Molecular Stability
- If the image of the point $ P(1, 0, 3) $ in the line joining the points $ A(4, 7, 1) $ and $ B(3, 5, 3) $ is $ Q(\alpha, \beta, \gamma) $, then $ \alpha + \beta + \gamma $ is equal to:
- JEE Main - 2025
- 3D Geometry
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is:
- JEE Main - 2025
- Number Systems
View More Questions