1. A spherical mirror is to be used to form an image, six times as tall as an ob

Question

1.

A spherical mirror is to be used to form an image, six times as tall as an object, on a screen positioned 4.0 m from the mirror.

(a) Describe the type of mirror required.

The mirror is a concave mirror and it has a focal length of m._______

(b) Where should the mirror be positioned relative to the object?

The object should be m in front of the mirror.

2. A convex mirror has a focal length of magnitude 7.77 cm.

(a) If the image is virtual, what is the object location for which the magnitude of the image distance is one third the magnitude of the object distance? (Enter distance in cm from the front of the mirror. If the image is real, enter NONE.)

cm

(b) Find the magnification of the image.

Explanation / Answer

1)    Since the image has to be collected onto a screen it must be a real image.
A real image is always inverted, so magnification is negative:
M = -6
But M = - di/do, so
do = di / 6 = 4.0 / 6 = 0.666 m

From conjugate points formula
1/f = 1/do + 1/di
f = do di / (do + di) = 0.666 x 4.0 / (0.666 + 4.0) = 0.570 m

Therefore
(a)The mirror has a focal length of 0.570 m
(b) The object should be 0.666 m in front of the mirror

2) u is the object distance and v is the image distance,

Given v/u = -(1/3) minus since the image is virtual.

u/v = -3

1/u + 1/v = 1/f

1 + u/v = u/f

1-3 = u / (7.77)

2*7.77 = u = 15.54cm
answer for (a) u = 15.54cm
===========================
(b) m = v/u = -(1/3) = -0.333
minus sign shows that the image is erect

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