A ray of light passes through a plane glass slab of thickness t and refractive index μ = 1.5. The angle between the incident ray and emergent ray will be:a)30°b)45°c)60°d)0°Correct answer is option 'D'. Can you explain this answer?

Question

A ray of light passes through a plane glass slab of thickness t and refractive index &#956; = 1.5. The angle between the incident ray and emergent ray will be:&#8203;a)30&#176;b)45&#176;c)60&#176;d)0&#176;Correct answer is option 'D'. Can you explain this answer?

Answer

The incident ray and emergent ray are parallel to each other but latteray displaced due to reflaction at two surfaces . So, the angle between them is Zero.

Answer

Explanation:

When a ray of light passes through a plane glass slab, it undergoes refraction twice.

First, when it enters the slab from air and second, when it emerges out of the slab into air.

The refractive index of the glass slab is given as 1.5.

The angle of incidence (i) and angle of emergence (e) are related to the angle of refraction (r) by Snell's law.

Snell's law states that n1 sin i = n2 sin r, where n1 and n2 are the refractive indices of the two media and i and r are the angles of incidence and refraction, respectively.

For the first refraction, the angle of incidence is i and the angle of refraction is r1.

For the second refraction, the angle of incidence is r2 and the angle of emergence is e.

Applying Snell's law twice, we get:

sin i = (1.5) sin r1

sin r2 = (1/1.5) sin e = (2/3) sin e

sin i = (2/3) sin e

Dividing the above two equations, we get:

sin r1/sin r2 = 3/2

sin r1 = (3/2) sin r2

As the angle between the incident ray and emergent ray is the sum of the angles of refraction, we have:

Angle between incident ray and emergent ray = r1 + r2

Angle between incident ray and emergent ray = r1 + (sin^-1((2/3)sin i))

Substituting sin r1 = (3/2) sin r2 in the above equation, we get:

Angle between incident ray and emergent ray = (3/2) sin r2 + (sin^-1((2/3)sin i))

Angle between incident ray and emergent ray = (3/2) (sin^-1((2/3)sin e)) + (sin^-1((2/3)sin i))

As sin^-1((2/3)sin e) and sin^-1((2/3)sin i) are acute angles, their sum is less than or equal to 90 degrees.

Therefore, the angle between the incident ray and emergent ray is less than or equal to 90 degrees.

Hence, option 'D' (0 degrees) is the correct answer as the angle between the incident ray and emergent ray is zero degrees, which means they are parallel.

Answer

The incident Ray and the emergent Ray , are parallel to each other if the medium is same on both sides of the glass slab so angle is 0 degree

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