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प्रश्न
In the figure, the optical fibre is l = 2 m long and has a diameter of d = 20 µm. If a ray of light is incident on one end of the fibre at angle θ1 = 40°, the number of reflections it makes before emerging from the other end is close to:
(Refractive index of fibre is 1.31 and sin 40° = 0.64)
विकल्प
55000
66000
45000
57000
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उत्तर
57000
Explanation:
Given:
Optical fibre length, l = 2 m
Diameter of the fibre, d = 20 µm
Angle of incidence at the fiber’s entrance θ1 = 40°
Refractive index of fibre, μ2 = 1.31
To find:
The total number of reflections inside the fibre.
Calculation:
Using Snell’s law:
`mu_1/mu_2 = (sintheta_2)/(sin40^circ)`, ...(The refractive index of air is µ1.)
`sintheta_2 = 1/1.31 sin40^circ`
θ2 = 29.39
θ = 90 − θ2
= 90 − 29.39
= 60.6 ...(θ as shown in the diagram)
tan θ = tan 60.6 = `x/d` ....(x is labelled in the diagram.)
x = (20 × 10−6) tan 60.6 = 35.5 µm
Number of total reflections;
n = `1/x`
= `(2m)/(35.5mum)`
= 56338
Therefore, the total number of reflections is approximately 56,338. Since this does not exactly match any option, we select the nearest available option, which is 57,000.
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