A large glass slab of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R ? [2010]

Question

A large glass slab $(μ = \frac{5}{3})$ of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R ? [2010]

Smart Achievers · Accepted Answer

(6)

In the figure, C = critical angle

In $∆ P O M$ , $\tan C = \frac{O M}{P M} = \frac{R}{8}$

$∵$ $\sin C = \frac{1}{μ} = \frac{3}{5}$ $∴$ $\tan C = \frac{3}{4}$

$∴$ $\frac{R}{8} = \frac{3}{4}$

$∴$ $R = \frac{3}{4} \times 8 = 6 cm$

Solution

Q.
A large glass slab $(μ = \frac{5}{3})$ of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R [2010]

Ans.
(6)

In the figure, C = critical angle

In $∆ P O M$ , $\tan C = \frac{O M}{P M} = \frac{R}{8}$

$∵$ $\sin C = \frac{1}{μ} = \frac{3}{5}$ $∴$ $\tan C = \frac{3}{4}$

$∴$ $\frac{R}{8} = \frac{3}{4}$

$∴$ $R = \frac{3}{4} \times 8 = 6 cm$

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Solution

Q. A large glass slab (μ=53) of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R [2010]

Ans. (6) In the figure, C = critical angle In ∆POM, tanC=OMPM=R8 ∵ sinC=1μ=35 ∴ tanC=34 ∴ R8=34 ∴ R=34×8=6 cm

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Q.
A large glass slab $(μ = \frac{5}{3})$ of thickness 8 cm is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius R cm. What is the value of R [2010]

Ans.
(6)

In the figure, C = critical angle

In $∆ P O M$ , $\tan C = \frac{O M}{P M} = \frac{R}{8}$

$∵$ $\sin C = \frac{1}{μ} = \frac{3}{5}$ $∴$ $\tan C = \frac{3}{4}$

$∴$ $\frac{R}{8} = \frac{3}{4}$

$∴$ $R = \frac{3}{4} \times 8 = 6 cm$