Please help by providing steps and some explanation so I can understand (2) An e

Question

Please help by providing steps and some explanation so I can understand

(2) An external rearview car mirror is convex with a radius of curvature R m. A truck is at do m away from the mirror. (a) Find the maximum and minimum of the magnification and when they occur. (b) Describe how the magnification changes as the truck is (i) approaching to and (ii) falling farther behind your car. (c) What if a rearview car mirror is concave? Describe how the image of the truck changes as it approaches to your car. Will a concave rearview mirror be useful or not? [12-4+4+4 Marks

Explanation / Answer

2. given, external rear view mirror is convex, radius of curvature = R

distance of truck = do

a. focal length of convex lens, f = -R/2

for object distance -u ( where u is +ve)

image distance is v

from mirrro equation

1/v - 1/u = 1/f

1/v = -2/R + 1/u = (R - 2u)/Ru

v = Ru/(R - 2u)

magnification = -v/u = R/(2u - R)

for maximum magnification, 2u - R is minimum, so u = R/2, m = infinite

for minimum magnification, 2u - R is maximum, so u = infinite, m = 0

b. rate of chang eof magnification wrt t is given by

dm/dt = R*d(2u - R)^-1/du = -2R(du/dt)/(2u - R)^2

so when truck is approaching, du/dt is -ve, hence dm/dt is +ve hence magnification increase4s when truck approaches

similiarly, magnification decreases when truck recedes

c. if rear view mirror is concave

then the magnification will decrease when the truck comes closer and the magnification will increase when it goes far

also, the image of the truck will always be inverted unless truck is closer than R/2 to the mirror and inverted image will not help as a rear wview image and hence concave mirror will not be useful as rear view mirror

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