Question

Statement-1: When light ray enter in a rectengular glass slab, at angle of incidence \(0<\theta<90\) then dispersion of light is not observer. Statement-2: In dispersion, a beam of white light refracts at different angles of refraction when it enter oblique in a medium. (1) Statement- 1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement- 1 (2) Statement- 1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1 (3) Statement-1 is True, Statement- 2 is False (4) Statement-1 is False, Statement-2 is True.

Short answer

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1.

Step-by-step solution

Analyze Statement-1

Statement-1 says that when light enters a rectangular glass slab at an angle of incidence between 0 and 90 degrees, dispersion is not observed. This is correct because a rectangular glass slab does not disperse light into its component colors as a prism does. The colors reunite after passing through the parallel surfaces of the slab.

Analyze Statement-2

Statement-2 states that in dispersion, a beam of white light refracts at different angles of refraction when it enters a medium obliquely. This is also correct because dispersion of light occurs due to the different wavelengths refracting at different angles, as each color has a unique index of refraction.

Correlate Both Statements

Since dispersion refers to the splitting of white light into its constituent colors, and a rectangular glass slab does not cause dispersion, the two statements talk about different contexts. Statement-1 talks about the lack of dispersion in a rectangular glass slab, while Statement-2 describes the phenomenon of dispersion in general.

Determine Relationship

Statement-2, while true in its own context, does not explain why dispersion is not observed in a rectangular glass slab. The geometric arrangement of the slab, with parallel sides, explains the lack of dispersion, not the principle described in Statement-2.

Choose Correct Option

Based on the analysis, both Statement-1 and Statement-2 are true, but Statement-2 does not correctly explain Statement-1.

Key concepts

Angle of Incidence

In optics, the angle of incidence is the angle between an incoming light ray and the perpendicular (normal) to the surface it strikes. This angle plays a crucial role in determining how light behaves as it encounters different materials. Specifically, when light enters a rectangular glass slab at an angle of incidence (\(0 < \theta < 90\)). Despite the light bending, or refracting, as it passes through the slab, all colors are refracted by the same amount given the parallel surfaces of the glass slab, thus no dispersion happens.
If you consider a ray of light entering a glass slab at an oblique angle, this means it hits the slab at an angle other than 90 degrees. This is typical in many real-world scenarios and essential in understanding how lenses and various optical devices work.

Refraction

Refraction is the bending of light as it passes from one medium to another. This change in direction occurs because light travels at different speeds in different materials. The amount of refraction depends on the angle of incidence and the indices of refraction of the materials. The general behavior can be described by Snell's Law: \( n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \),
where:

• \( n_1 \) and \( n_2 \) are the indices of refraction of the first and second medium, respectively.
• \( \theta_1 \) is the angle of incidence.
• \( \theta_2 \) is the angle of refraction.

When light transitions from air (less dense) into glass (more dense), it slows down and bends towards the normal. Upon exiting the glass slab back into the air, it speeds up and bends away from the normal. The extent and direction of this bending are critical in both focusing lenses and designing various optical instruments. This consistent bending can lead to different optical effects, including magnification, focusing, and in specific structures like prisms, dispersion.

Rectangular Glass Slab

A rectangular glass slab is a block of glass with parallel sides. When light enters and exits through these parallel sides, it undergoes refraction at both surfaces. However, since the surfaces are parallel, the emerging light ray is parallel to the incident ray and all colors converge back together, which prevents dispersion. Dispersion is the splitting of light into its constituent colors and typically occurs in prisms where the sides are not parallel.
For instance, a prism with angled surfaces can disperse light because different colors (wavelengths) of light refract (or bend) by different amounts. Blue light bends more than red light due to its shorter wavelength. However, in a rectangular glass slab these effects cancel each other out due to the parallelism of the surfaces. Hence, although the light undergoes refraction, it doesn’t spread out into different colors.

• When light enters at an angle other than 90 degrees, it bends towards the normal upon entering the glass (denser medium).
• It bends away from the normal when exiting back into the air (less dense medium).
• This two-fold bending ensures the emergent ray stays parallel to the incident ray, ensuring a lack of dispersion.