Question

What can be the largest distance of an image of real object from a convex mirror of radius of curvature 20 cm (pls explain also ):
a. 10cm
b. 20cm
c.infinity
d. zero

Answer 1

Answer:  Maximum distance = option (a) 10 cm.

Explanation:

It is given in the question that it is a convex mirror,

we have , R = 20 cm, ∴ f = +10 cm

u = -x ; v = ? ; f = +10 cm

we know that formula for mirror is

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

$\frac{1}{10}$ = $\frac{1}{v}$ - $\frac{1}{x}$

$\frac{1}{v}$ = $\frac{1}{10}$ + $\frac{1}{x}$   ..................equation 1

$\frac{1}{v}$  = $\frac{10+x}{10x}$

∴v = $\frac{10x}{10+x}$

differentiating the above expression, we get

$\frac{dv}{dx}$ = $\frac{10(10+x) - 10x.(1)}{(10+x)^{2} }$

$\frac{dv}{dx}$  = $\frac{100}{(10+x)^{2} }$

$\frac{dv}{dx}$ = 0 , where x = ∞

Now,

$\frac{d^2v}{dx^2}$ = $\frac{100x-2}{(10+x)^{2} }$

at x = ∞,  $\frac{d^2v}{dx^2}$  =  -∞ < 0,  so at x =  ∞, v will be maximum

on putting x =  ∞ in equation 1 , we have

$\frac{1}{v_{max} }$ = $\frac{1}{10}$

$v_{max}$ = 10 cm.

∴ Image will be formed at focus.

Answer 2

Thus the largest distance of an image from a convex mirror is 10 cm.

Option (A) is correct.

Explanation:

We are given that:

Radius of curvature = 20 cm

To find: Largest distance of an image

Solution:

In a convex mirror image is formed between focal length and mirror.

So the maximum distance is f i.e. focal length of the mirror.  

Now

f = 20 / 2 = 10 cm

Thus the largest distance of an image from a convex mirror is 10 cm.