Question

A convex mirror has been cut out of a sphere represented by the equation $x^2+y^2+z^2=25$ where $x,y,z$ are in $\text{cm}$. If a parallel beam of light, after reflection from the mirror appears to intersect at the focal point of the mirror, then its focal length is:

• A. $+5\text{cm}$
• B. $-5\text{cm}$
• C. $+2.5\text{cm}$
• D. $-2.5\text{cm}$

Answer 1

The correct option is C $+2.5\text{cm}$

As a parallel beam of light after reflection from the mirror appears to intersect at the focal point, thus, the mirror is convex.
Given the equation of the sphere of which the convex mirror is a part
$x^2+y^2+z^2={25}^2$
Comparing with $x^2+y^2+z^2=R^2$, we get the radius of curvature,
$R=5\text{cm}$

For convex mirror,
$R=+5\text{cm}$
Now,
Focal length,
$f=\frac{R}{2}=\frac{+5}{2}=+2.5\text{cm}$