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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?
Verified Answer
A ray of light passes through a plane glass slab of thickness t and re...
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.
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A ray of light passes through a plane glass slab of thickness t and re...
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.
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A ray of light passes through a plane glass slab of thickness t and re...
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.
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