A horizontal cylindrical tank 2.02 m in diameter is half full of water. The spac

Question

A horizontal cylindrical tank 2.02 m in diameter is half full of water. The space above the water is filled with a pressurized gas of unknown refractive index. A small laser can move along the curved bottom of the water and aims a light beam toward the center of the water surface (see the figure below). You observe that when the laser has moved a distance S = 1.01 m or more (measured along the curved surface) from the lowest point in the water, no light enters the gas. (a) What is the index of refraction of the gas? (b) How long does it take the light beam to travel from the laser to the rim of the tank for the following? (i) when S > 1.01 m (ii) when S

Explanation / Answer

Salad bowl can be considered as a convex mirror.
Focal length, f = R/2, R is the radius of curvature.
f = 39/2 = 19.5 cm
For a convex mirror, f is taken as negative.
Object distance, u = 47 cm
Take v as the image distance.

Using the equation, 1/f = 1/u + 1/v,
1/v = 1/f - 1/u
v = uf / (u - f)
= [(47 x (-19.5)] / [47 - (-19.5)]
= - 13.78 cm.

a)
Since v is negative, the image is formed behind the mirror at a distance of 13.78 cm from the center.

b)
Image size/object size = -(v/u)
Image size = object size x [-(v/u)]
= 2.6 x - [(-13.78)/47]
= 0.76 cm

c)
Magnification, m = - (v/u)
= - [(-13.78)/47]
= 0.29
Since the sign of the magnification is positive, the image is erect.

d)
The image is virtual since it is formed behind the mirror.

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