Please provide a detail explanation. A small statue has a height of 3.5 cm and i

Question

Please provide a detail explanation.

A small statue has a height of 3.5 cm and is placed in front of a concave minor. The image of the statue is inverted, 1.5 cm tail, and is located 13 cm in front of the mirror. Find the focal length of the mirror. The figure shows a ray of light that originates is an aquarium. It travels through water, is incident on the glass side, and emerges into the air. Ignore any partial reflections. Note: The figure is not drawn to scale. Calculate the angle alpha, beta. Calculate the smallest angle of incidence in the water for which no light emerges into air?

Explanation / Answer

1. apply for concave mirror 1/f = 1/u + 1/v

where u is object distance

v is image distance

f is focal length

also magnification m = -v/u = -v'/u' = 1.5/3.5 = 0.428

so

v = 0.428 u

as v   = 13 cm

u = 13/0.428 = 30.27 cm

so

f = uv/u+v

f = 30.27 * 13/(30.27-13)

f = 22.78 cm

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apply snells law as na sinA = nb sin B

so here for water glass surface

1.33 sin 30 = 1.45 sin Alpha

sin alpha = 0.665/1.45 = 0.4586

Alpha   = 27.29 deg

-------------------------

use snells law for glass air interface

sin B = 1.45 * sin 27.29/1.

sin B = 0.665

Beta = B = 41.68 deg

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