Question

a car uses convex mirror of curvature 1.2 m as its rear view mirror. a minibus of cross section 2.2m ×2.2m is 6.6m away from the mirror. estimate the image size​

Answer 1

Answer:

The size of the image will be $0.18 \text{ m}\times 0.18 \text{ m}$

Explanation:

Given radius of curvature of the convex mirror

$R=1.2$ m

Therefore, focal length of the the mirror

$f=\frac{R}{2}$

$\implies f=\frac{1.2}{2}$

$\implies f=0.6$m

Distance of the object $u=-6.6$ m

Let the distance of the image be u

Since convex mirror forms a virtual image, the signs of object and images will be opposite

Using

$\boxed{\frac{1}{f}=\frac{1}{u}+\frac{1}{v}}$

$\implies \frac{1}{0.6}=\frac{1}{-6.6}+\frac{1}{v}$

$\implies \frac{1}{v}=\frac{1}{0.6}+\frac{1}{6.6}+$

$\implies \frac{1}{v}=\frac{6.6+0.6}{0.6\times 6.6}$

$\implies \frac{1}{v}=\frac{7.2}{0.6\times 6.6}$

$\implies \frac{1}{v}=\frac{12}{6.6}$

$\implies v=\frac{6.6}{12}$

$\implies v=0.55$ m

Therefore, magnification due to the convex mirror

$=-\frac{v}{u}$

$=-\frac{0.55}{-6.6}$

$=\frac{5}{60}$

$=\frac{1}{12}$

Thus the size of a 2.2 m object will be

$=\frac{1}{12}\times 2.2$

$=0.18$ m

Thus, the size of the image will be $0.18 \text{ m}\times 0.18 \text{ m}$

Hope this helps.