Question

A dentist uses a mirror in front of a decayed tooth at a distance of 4cm from the tooth to get a 4 times magnified image. Use mirror formula to find the focal length of the mirror used. Is m=+4 or m= -4? How do we know?

Answer 1

The focal of lens depends on curvature of the lens and the difference between the curved surfaces, as given by the lensmaker equation .
$\frac{1}{f}=(n-1)[\frac{1}{R_1}+\frac{1}{R_2}+\frac{(n-1)d}{n{R}_1{R}_2}]$
f is the focal length of the lens,
n is the refractive index of the lens material,
$R_1$ is the radius of curvature of the lens surface closest to the light source,
$R_2$ is the radius of curvature of the lens surface farthest from the light source, and d is the thickness of the lens between the curved surfaces
If you reduce d then the focal length increases. If you mean making the lens less curved and hence thinner, then the curvature of the interfaces $\left(R_{1}and{R}_2\right)$ will increase and hence the focal length will increase.