If the refractive index of the material of a prism is \(cot\bigg(\frac{A}{2}\bigg)\), where A is the angle of the prism, then the angle of minimum deviation will be:
- \(π-3A\)
- \(π-2A\)
- \(A\)
- \(\frac{A}{2}\)
The Correct Option is B
Solution and Explanation
To find the angle of minimum deviation \( \delta_{\text{min}} \):
Step 1. Given Relation:
\( \cot \frac{A}{2} = \frac{\sin \frac{A + \delta_{\text{min}}}{2}}{\sin \frac{A}{2}} \)
Step 2. Rearrange and Simplify: Take the cosine of both sides:
\( \cos \frac{A}{2} = \sin \frac{A + \delta_{\text{min}}}{2} \)
Step 3. Solve for \( \delta_{\text{min}} \): Equate the arguments, giving:
\( \frac{A + \delta_{\text{min}}}{2} = \frac{\pi}{2} - \frac{A}{2} \)
- Solving, we get:
\( \delta_{\text{min}} = \pi - 2A \)
Thus, the angle of minimum deviation is \( \pi - 2A \).
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Reflection of Light
When a light ray falls on any object, it is bounced back from the object. This process is known as the Reflection of light. The light reflected from the object falls into our eyes, making the object visible to us. All the things we see around us are because of reflection.
The reflection of light depends on the type of object. A polished or smooth surface reflects most of the light falling on it, while a rough surface absorbs some amount of light and reflects back the rest of the light. The direction of reflected rays depends upon the surface of the object.
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