1)You are standing 3.2m from a convex security mirror in a store. You estimate t

ID: 2299102 • Letter: 1

Question

1)You are standing 3.2m from a convex security mirror in a store. You estimate the height of your image to be half of your actual height.

Estimate the radius of curvature of the mirror.

Express your answer using two significant figures.

2)The image of a distant tree is virtual and very small when viewed in a curved mirror. The image appears to be 13.8cm behind the mirror.

What is its radius of curvature?

3) The critical angle for a certain liquid-air surface is 43.9.

What is the index of refraction of the liquid?

We know that mirror equation is,

1/f = 1/v + 1/u

and m= hi/ho = -v/u

where v is image distance and u is object distane

also f = R/2 ; R = radius of curvature

1) u = -3.2 m

m= -v/u => 1/2 = -v/-3.2 => v = 1.6 m

1/f = 1/1.6 - 1/3.2

=> f = 3.2 m

Hence R = 2f = 6.4 m

2) virtual image means +ve magnification => v = 13.8 cm

u = infinity

1/f = 1/v +1/u => 1/f = 1/13.8 + 1/infinity => f = 13.8 cm

R = 2f = 2*13.8 = 27.6 cm

3.) if critical angle is denoted by C

then refractive index n = 1/ SinC

so here , n = 1/sin(43.9) = 0.69

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