Question 170: Ray Optics

Question

An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s, the speed and direction of the image will be :

Accepted Answer

From lens equation
$${1 \over v} - {1 \over u} = {1 \over f}$$
$${1 \over v} - {1 \over {\left( { - 20} \right)}} = {1 \over {\left( {.3} \right)}} = {{10} \over 3}$$
$${1 \over v} = {{10} \over 3} - {1 \over {20}}$$
$${1 \over v} = {{197} \over {60}};v = {{60} \over {197}}$$
m = $$\left( {{v \over u}} \right)$$ = $${{\left( {{{60} \over {197}}} \right)} \over {20}}$$
velocity of image wrt. to lens is given by
v
I/L
= m
2
v
O/L
direction of velocity of image is same as that of object
v
O/L
= 5 m/s

Answer

1.16 $$ 	imes $$ 10
–3
m/s towards the lens

Answer

2.26 $$ 	imes $$ 10
–3
m/s away from the lens

Answer

3.22 × 10
–3
m/s towards the lens

Answer

0.92 $$ 	imes $$ 10
$$-$$3
m/s away from the lens

Ray Optics

An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s, the speed and direction of the image will be :

Choose the correct answer: