Shown in the figure is one corner of a rectangular box filled with oil (n = 1, 4

Question

Shown in the figure is one corner of a rectangular box filled with oil (n = 1, 46) surrounded by air, A laser beam starts 10 cm from side A of the container and enters the oil at position x = 30 cm. A. Find the angle of incidence theta_1 and angle of refraction theta_2 at the first surface, (2-3) B. Find the angle of incidence theta_3 at the second surface. (3) C. Explain total internal reflection. When does it happen? Find the critical angle of the oil-air interface. (3+2) D. Find the angle of refraction or reflection (call it theta_4) at the second surface. Show a detailed picture (3+2)

Explanation / Answer

A)

1= tan^-1(30cm/10cm) = 71.57 deg

By Snell’s law,

n1sin1 = n2sin2

2=sin^-1( n1sin1)/n2 = sin^-1(sin71.57*1/1.46) = 40.53 deg

B)

Since 3 and 2 are angle between two parallel lines,

3= 2= 40.53 deg

C)

Total reflection occurs when a light rays travels from denser medium to rarer medium. At the boundary of two media there is a critical angle at which refraction angle is equal to 90 deg in the second medium. Beyond this critical angle light rays passing through the second medium totally reflected in the first medium and there is no light ray travelling in the second medium. This phenomenon is called as total reflection.

D)

By Snell’s law,

n3sin3 = n4sin4

4=sin^-1( n3sin3)/n4 = sin^-1(sin40.53*1.46/1.0) = 71.57 deg

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