Question

Figure shows a cylinder of height H and radius R. A parallel horizontal beam of light is incident on
cylinder. Draw diagram of shadow of cylinder on screen and find its area.
​

Answer 1

Answer:

Figure-(I) shows how for rays nearer to base are refracted but as rays move away from base, they fall nearer and after a certain distance above base, all rays are internally reflected.

So, we have to find the distance x where there is no light. As on increasing height rays fall nearer to the prism, so we have to find where will the ray for critical angle of incidence will intersect base line. And inside that point there will be no illumination as for larger angle of incidence , rays are internally reflected.

From figure-2, it is clear that i=C=critical angle and refracted ray for this goes perpendicular to normal which is radius OA here. Refracted ray is AB.

i=C=sin

1

μ

1

=sin

−1

2

3

=60

o

From ΔOAB:−

cosi=

OB

OA

=

R+x

R

⟹cos60

o

=

2

1

=

5+x

5

⟹x=5cm

Answer 2

Answer:

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