When a person stands 40 cm in front of a cosmetic (concave)spherical mirror,the upright image is twice the size of the object.What is the focal length of the mirror?
A)27 cm
B)40 cm
C)80 cm
D)160 cm

Question

Quizplus · Accepted Answer

We can use the mirror equation here:

1/f = 1/d_o + 1/d_i

where f is the focal length, d_o is the object distance (40 cm), and d_i is the image distance (we don't know this yet).

We also know that the magnification is 2, meaning:

m = -d_i/d_o = 2

Solving for d_i in terms of d_o, we get:

d_i = -2d_o

Now we can plug in the values into the mirror equation:

1/f = 1/40 + 1/(-2*40)

Solving for f, we get:

f = -80 cm

However, we need to take the absolute value of f since it is a positive physical quantity. Therefore:

|f| = 80 cm

So the focal length of the mirror is 80 cm, which corresponds to choice C.

When a Person Stands 40 Cm in Front of a Cosmetic