Problem 2898 - JEE Physics

Question

A ray of light is incident on an equilateral glass prism placed on a horizontal table. For minimum deviation which of the following is true? (A) RS is horizontal (B) either \(\mathrm{PQ}\) or \(\mathrm{RS}\) is horizontal (C) QR is horizontal (D) PQ is horizontal

Step-by-Step Solution

Answer

For minimum deviation in an equilateral glass prism, the angle of incidence and angle of emergence must be equal and symmetrical with respect to the base of the prism. In this case, the side PQ should be horizontal. Therefore, the correct statement is (D) PQ is horizontal.

Step 1: Define minimum deviation

Minimum deviation is the smallest angle through which a ray of light changes its direction when passing through a prism. This occurs when the angle of incidence and angle of emergence are equal. Step 2: Draw a diagram

Step 2: Draw a diagram

Draw an equilateral triangle (with all angles equal to 60 degrees) representing the prism on a horizontal table. Mark points P, Q, and R at different corners of the triangle. Show the incident light ray entering the prism at point P, refracting inside, and emerging at point R. Draw QRS and PQ parallel to the table. Step 3: Analyze the given options

Step 3: Analyze the given options

We have to determine which of the following options is true for minimum deviation: (A) RS is horizontal (B) either PQ or RS is horizontal (C) QR is horizontal (D) PQ is horizontal Step 4: Relation between minimum deviation and horizontal sides

Step 4: Relation between minimum deviation and horizontal sides

For minimum deviation, the angle of incidence and angle of emergence have to be equal and thus symmetrical with respect to the base of the prism. In an equilateral prism, the angle of refraction inside the prism will be equal for both surfaces (PQ and RS). Hence, the incidence surface and emergence surface should be symmetrical to have equal angles of incidence and emergence. Step 5: Choose the correct option

Step 5: Choose the correct option

For the prism to have symmetrical angles for minimum deviation, the side PQ should be horizontal. Thus, the answer is: (D) PQ is horizontal

Key Concepts

Equilateral Prism

An equilateral prism is one where all the sides are of equal length and all the angles between the prism faces are 60 degrees. This kind of prism is symmetrical and easy to analyze in optics due to its consistent geometry. Understanding an equilateral prism is crucial when studying light behavior, as its equal angles lead to predictable patterns in light refraction and deviation.
When light enters an equilateral prism, it helps to consider the inherent symmetry of this shape. This symmetry simplifies calculations and predictions of how light travels through such a prism.

Angle of Incidence

The angle of incidence is critical for determining how a ray of light will behave when it strikes a surface, like a prism's face. It is the angle between the incoming light ray and a line perpendicular to the surface at the point of contact (the normal).
The angle of incidence in an equilateral prism affects how much and in which direction the light is bent. For the condition of minimum deviation, this angle must be the same as the angle of emergence, emphasizing a balanced entry and exit of light within the prism.
In practical terms, by adjusting the angle of incidence, particularly in an equilateral prism setup, we can manage the dispersion and the path that light will take through the prism.

Angle of Emergence

Just like the angle of incidence, the angle of emergence refers to the angle between the outgoing refracted ray and the normal to the surface from which the light exits. The angle of emergence is crucial in determining the overall direction in which the light eventually moves after passing through the prism.
For an equilateral prism experiencing minimum deviation, the angle of emergence equals the angle of incidence. This condition ensures that the ray of light travels symmetrically through the prism, minimizing the overall change in direction, known as deviation.
This balance between incidence and emergence angles is vital for applications where precise light direction and minimal deviation are required, such as in optical instruments.

Refraction in Prisms

Refraction is the bending of light as it passes from one medium into another and is a central concept when studying prisms. In an equilateral prism, refraction occurs at both the entry and exit points, with the light bending towards the normal at entry and away from the normal at exit.
When discussing refraction in prisms, the laws of refraction apply; specifically Snell's Law, which provides the relationship between the angles and the refractive indices of the mediums involved. For an equilateral prism, the refractive process is symmetrical if the angles of incidence and emergence are equal.
This symmetrical condition is sought for achieving minimum deviation, where the light path through the prism is optimized to reduce the degree of deviation experienced. This property is extensively used in designing optical systems that require precise light paths and minimal dispersion.