Question

A driving mirror having radius of curvature $100\text{cm}$ and length over the curved surface is $10\text{cm}$. If the eye of the driver is assumed to be at a large distance, then the field of view in radians is: (consider paraxial rays only and small mirror operator)

• A. $0.2$
• B. $4$
• C. $3$
• D. $5$

Answer 1

The correct option is A $0.2$


Considering parallel paraxial rays incident from very far objects $\left(\infty \right)$ the angle $\theta$ will be very small for small aperture mirror.
$\Rightarrow \tan \theta \approx \theta$
Also for very small mirror aperture, the curved surface $PM$ can be assumed to be vertical.
$PM=10\text{cm}$
$NF=\frac{R}{2}=\frac{100}{2}=50\text{cm}$
$NF\perp PM$ and bisects the angle $PFM$.
$\therefore PN=NM=\frac{PM}{2}=5\text{cm}$
From $\Delta PNF$,
$\tan \theta =\frac{PN}{NF}$
$\Rightarrow \theta =\frac{5}{50}=0.1\text{rad}$
$\Rightarrow$ Field of view is $2\theta$ i.e. $0.2\text{rad}$.