Question

A small insect is walking with a speed of 2 mm per second towards the pole of concave mirror
of focal length 20 cm. What is the speed of the image of the insect formed by the mirror when
the insect is at a distance of 60 cm from the mirror?​

Answer 1

Answer:

twice !

Explanation:  v = uf/u-f = 4.5

1/f = 1/v + 1/u .....eq(1)  on deff.....

o = (1/v²)dv/dt + (1/u²)du/dt ...... as  v= 4.5 and u = 60 and du/dt = 2 cm

dv/dt = 24.75/1800

dv/dt = 0/01375 cm/s

Answer 2

Answer:

The speed of the image of an object is 0.05cm/s.

Explanation:

Given:

V = -0.2cm/s

u = 60cm

f = 20cm

Here,

The distance of the object from the mirror is denoted by u.

The distance of the image from the mirror is denoted by v.

The focal length of the mirror is denoted by f.

The speed of the object is denoted by S.

The speed of the image of an object is denoted by V.

Now,

By the equation,

$\frac{1}{f} =\frac{1}{u} +\frac{1}{v} \\\frac{1}{20} =\frac{1}{60} +\frac{1}{v} \\v = 30cm$

Then,

$\frac{1}{f} =\frac{1}{u} +\frac{1}{v}$                                  .....eq(1)  

On differentiation of both side,

$0 = \frac{1}{u^{2} } \frac{du}{dt} +\frac{1}{v^{2} } \frac{dv}{dt} \\0=\frac{1}{u^{2}} S+\frac{1}{v^{2}} V\\0=\frac{1}{60^{2}} (-0.2)+\frac{1}{30^{2}} V\\V=0.05cm/s$  

So, the speed of the image of an object is 0.05cm/s.