1. Given: M = -5 di = 12 feet do =? f = ?
It is desired to cast the image of a lamp, magnified 5 times, upon a wall 12 feet from the mirror. What kind of spherical mirror is required and where should it be placed?
M is negative, di is positive
because the image is real
Object should be placed 2.4 ft from a concave mirror of 2.0 ft focal length
Given:
M = -5
di = 12 feet
do =?
f = ?
M = - di/do
-5 = -12/do
do = 2.4 ft 1 1 1 1 1 1 = + = +
2.4 12 f do di f
f = 2 ft

2. M = - di/do 1/6 = -di/do do = - 6di  do = 12 cm
2. A convex spherical mirror of focal length 2.4 cm produces an image 1/6 the size of an object. Where is the object?
M is positive because
the image is virtual
Given:
M = +1/6
f = cm
do = ? 1 1 1 = + f do di
f is negative because
the mirror is convex 1 1 1 = +
M = - di/do
1/6 = -di/do
do = - 6di di
-2.4
-6di
Cross multiply 1 1 -6 = +
-2.4
-6di
-6di 1
- 5 =
 do = 12 cm
di = -2 cm
-2.4
- 6di

3. M = - di/do M1 = -7.5/30 = -.25 M2 = - -3.75/6 = +.625
3. Two lenses, having focal lengths of +6 cm and -10 cm, are spaced 1.5 cm apart. Locate and describe the image of an object 30 cm in front of the + 6 cm focal length lens. 1 1 1 1 1 1
Given:
f1 = +6 cm
f2 = - 10 cm
x = 1.5 cm
do1 = 30 cm = + = + f1
do1
di1 f2
do2
di2 1 1 1 1 1 1 = + = + 6 30
di1
-10 6
di2
di1 = 7.5 cm
di2 = cm
M = - di/do
M1 = -7.5/30 = -.25
M2 = /6 = +.625
do2 = |x – di1|
do2 = | 1.5 – 7.5| = 6 cm

4. di2 = -3.75 cm  final image is 3.75 cm from lens 2 and is virtual
Mcombo = (M1)(M2) = (-.25)(+.625) = -.156
 final image is inverted and smaller