Question

A driving mirror consists of a cylindrical mirror of radius of curvature $10\text{cm}$ and the length of the curved surface of the mirror is $10\text{cm}$. If the eye of the driver is assumed to be at a great distance from the mirror, then the field of view (in $\text{radians}$) is:
[Assume paraxial approximation]

• A. $2.0$
• B. $4.0$
• C. $3.0$
• D. $5.0$

Answer 1

The correct option is A $2.0$


Consider parallel rays coming from a large distance incident on the edges of the mirror. After reflection, they will appear to diverge from the focus.
& we know that, focal length, $f=\frac{R}{2}=5\text{cm}$

Field of view is defined as the angle subtended by the two rays (reflected from the edges of the mirror's curved surface) at the focus

$\theta =\frac{\text{arc}}{\text{radius}}=\frac{10\text{cm}}{5\text{cm}}=2\text{rad}$

Hence, option $\left(a\right)$ is the correct answer.