1) An object that is 26.0 cm in front of a convex mirror has an image located 15

Question

1) An object that is 26.0 cm in front of a convex mirror has an image located 15.0 cm behind the mirror. What is the distance of the image when the object is 28.0 cm in front of the mirror?

2) A section of a sphere is mirrored on both sides. If the magnification of an object is +3.60 when the section is used a concave mirror, what is the magnification of an object at the same distance in front of the convex side?

**Please make sure you include the proper algebraic sign for the focal lengths, the distance of the objects, the distance of the images etc...**

Explanation / Answer

1)
do = 26.0 cm
di = -15.0 cm
f = ?

We know,
1/f = 1/di + 1/do
1/f = - 1/15.0 + 1/26.0
f = - 35.5 cm

Now,
do = 28.0 cm
di = ?

1/f = 1/di + 1/do
- 1/35.5 = 1/di + 1/28.0
di = - 15.65 cm
distance of the image, = 15.65 cm behind the mirror.

2)
M = -di/do
- 3.6*do = di
We know,
1/f = 1/di + 1/do
1/f = - 1/3.6*do + 1/do ------1

Now in case of convex mirror,
Let the Magnification be M
M = -di/do
di = - M*do

f' = -f
1/f = 1/di + 1/do
-1/f = -1/M*do + 1/do
1/3.6*do - 1/do = -1/M*do + 1/do
1/3.6 - 1 = -1/M + 1
M = 0.58
Magnification of an object , M = 0.58

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