A ray of light falls on a transparent glass slab of...

A ray of light falls on a transparent glass slab of refractive index 1.62. What is the angle of incidence, if the reflected ray and refracted ray are mutually perpendicular? (a) $\tan ^{-1}(1.62)$ (b) $\tan ^{-1}\left(\frac{1}{1.62}\right)$ (c) $\frac{1}{\tan ^{-1}(1.62)}$ (d) None of these

A ray of light falls on a transparent glass slab of refractive index 1.62. What is the angle of incidence, if the reflected ray and refracted ray are mutually perpendicular?
(a) $\tan ^{-1}(1.62)$
(b) $\tan ^{-1}\left(\frac{1}{1.62}\right)$
(c) $\frac{1}{\tan ^{-1}(1.62)}$
(d) None of these

Key Concepts

Snell's Law

Snell’s Law is a fundamental principle in optics that relates the angle of incidence to the angle of refraction when a light ray passes from one medium to another with a different refractive index. It establishes that the ratio of the sines of these angles is equal to the inverse ratio of the refractive indices, allowing one to determine how much the light ray bends at the interface.

Law of Reflection

The Law of Reflection states that when a light ray strikes a surface, the angle of incidence is equal to the angle of reflection. This concept is critical for understanding how light behaves upon encountering reflective surfaces, ensuring that the incident and reflected rays mirror each other with respect to the normal at the point of incidence.

Orthogonal Relationship Between Rays

When two rays, such as the reflected and refracted rays, are mutually perpendicular, a specific geometric relationship arises. This condition creates a link between the angles involved, which can be exploited mathematically (often involving trigonometric relationships) to relate the angle of incidence to the refractive index of the medium.

Trigonometric Relationships in Optics

Trigonometric functions, particularly the tangent function and its inverse, are often employed in optics to relate the angles of incidence and refraction to the refractive indices of different media. These relationships are useful in solving problems where geometrical conditions, such as perpendicularity of rays, impose additional constraints on the angles.

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