Homework #10 (chapter 40): Mirrors and Lenses

Exercise 1:

The speed v can be expressed as Δo/Δt. With i=-o for a plane mirror: v= Δo/Δt = -Δi/Δt

a) In your own reference frame the speed at which your mirror image is moving toward you is Δo/Δt – (-Δi/Δt) = 2v.

b) In the reference frame of the room, the image is moving at speed -Δi/Δt = v.

Exercise 13:

f = 35.0/2 cm

m = 2.7 = -i/o è i = -2.7 o

1/o + 1/i = 1/f

1/o -1/(2.7 o) = 1/f

1.7/(2.7 o) = 1/f è o = (1.7/2.7) f = (1.7/2.7) 35.0/2 cm = 11.0 cm

Exercise “eye”

n_eye = 1.34

n_air = 1.00

o = ∞

r = 0.78 cm

Use the equation for spherical refracting surfaces :

n_air / o + n_eye / i = (n_eye – n_air) / r

è i = r n_eye / (n_eye – n_air) = 0.78 cm*1.34 / (1.34-1.00) = 3.07 cm

The image forms 3.07 cm from the cornea, i. e. (3.07-2.30) cm = 0.77 cm behind the retina. The additional refraction by the lens is necessary to focus an image of an object at infinite distance on the retina. Note, however, that most of the refraction occurs at the cornea.

Exercise 37:

a) [a] 1/o + 1/i = 1/f; with o = ∞, i = 2.50 cm è f = 2.50 cm

[b] 1/o’ + 1/i = 1/f’; with o’ = 36 cm, i = 2.50 cm è f’ = 2.34 cm

b) smaller (see lens maker’s equation)