Question

A ray incident on a glass prism undergoes minimum deviation when:
incident angle is equal to the angle of refraction
refraction angle equals 90o
incident angle equals 90o
incident angle is equal to the angle of emergency

Answer 1

Answer on Question 46517, Physics, Optics

Question:

A ray incident on a glass prism undergoes minimum deviation when:

- incident angle is equal to the angle of refraction;

- refraction angle equals $90{}^{\circ}$ ;

- incident angle equals $90{}^{\circ}$ ;

- incident angle is equal to the angle of emergency.

Solution:

Let the refracting angle of a glass prism is equal $\varepsilon$ , the angle of deviation of a ray is equal $\angle KBC = D$ . Consider triangle MBN, we have:

$$D = \alpha_ {1} - \beta_ {1} + \alpha_ {2} - \beta_ {2} = (\alpha_ {1} + \alpha_ {2}) - (\beta_ {1} + \beta_ {2});$$

From consideration of triangle MPN we have:

$$\varepsilon = \beta_ {1} + \beta_ {2};$$

Therefore we obtain:

$$\mathrm {D} = \alpha_ {1} + \alpha_ {2} - \varepsilon .$$

From the last formula we can see that the angle of deviation of a ray has a minimum value when $\alpha_{1} = \alpha_{2}$ .

Answer:

A ray incident on a glass prism undergoes minimum deviation when incident angle is equal to the angle of refraction.

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