Question

shaving/makeup mirrors typically have one flat and one concave (magnifying) surface. you find that you can project a magnified image of a light - bulb onto the wall of your bathroom if you hold the mirror 1.8 m from the bulb and 3.5 m from the wall. what is the focal length of the mirror?

a. 5.7 m
b. 5.9 m
c. 3.5 m
d. 7.4 m
e. 1.2 m

Explanation:

Step1: Identify object and image distances

The object distance $u = 1.8$ m (distance from bulb to mirror), and the image distance $v=3.5$ m (distance from mirror to wall).

Step2: Apply mirror formula

The mirror formula is $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$. Substitute $u = 1.8$ m and $v = 3.5$ m into the formula: $\frac{1}{f}=\frac{1}{1.8}+\frac{1}{3.5}$. First, find a common - denominator for the right - hand side. The common denominator of 1.8 and 3.5 is $1.8\times3.5 = 6.3$. Then $\frac{1}{f}=\frac{3.5 + 1.8}{6.3}=\frac{5.3}{6.3}$.

Step3: Solve for focal length $f$

Cross - multiply to get $f=\frac{6.3}{5.3}\approx1.2$ m.

Answer:

e. 1.2 m