A prism having an apex angle 4^∘ and refractive index 1.5 is located in front of a vertical plan

step 1 In this question, a prism having apex angle is 4 degree, the Pax angle is 4 degree, this angle i

A prism having an apex angle 4^∘ and refractive index 1.5 is...

A prism having an apex angle $4^{\circ}$ and refractive index $1.5$ is located in front of a vertical plane mirror as shown in figure. Through what total angle is the ray deviated after reflection from the mirror?
(a) $176^{\circ}$
(b) $4^{\circ}$
(c) $178^{\circ}$
(d) $2^{\circ}$

Key Concepts

Reflection at a Plane Mirror

Reflection at a plane mirror involves the change in direction of a light ray when it bounces off a flat reflective surface. The law of reflection governs this process, stating that the angle of incidence is equal to the angle of reflection. In optical systems combining mirrors and prisms, the mirror introduces an additional deviation which must be factored in with the deviations due to refraction.

Apex Angle

The apex angle of a prism is the angle between its two refracting surfaces. It is a crucial parameter in determining the amount of deviation experienced by a light ray entering and exiting the prism. Small apex angles result in minimal deviation, while larger apex angles can lead to more significant bending of the light path.

Refraction

Refraction is the bending of light when it passes from one medium to another with a different refractive index. This change in speed causes the light ray to change direction, and the extent of bending is determined by Snell’s Law, which correlates the angles of incidence and refraction with the refractive indices of the two media.

Prism

A prism is an optical element with flat, polished surfaces that refract light. The deviation of a light ray passing through a prism is influenced by the prism’s geometry (notably its apex angle) and its refractive index. The interplay between these factors dictates how much the light ray is bent as it traverses the prism.

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