Question 46: Ray Optics

Question

Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from $${{25} \over 3}$$ m to $${{50} \over 7}$$ m in 30 s. What is the speed of the object in km per hour?

Accepted Answer

Focal length of a convex mirror, $$f = {R \over 2} = {{20} \over 2}$$ m = 10 m
For first object, $${v_1} =  + {{25} \over 3}$$ m, $$f =  + 10$$ m
Using mirror formula $${1 \over v} + {1 \over u} = {1 \over f}$$
$$	herefore$$ $${1 \over {(25/3)}} + {1 \over {{u_1}}} = {1 \over {10}}$$ or $${1 \over {{u_1}}} = {1 \over {10}} - {3 \over {25}}$$
or $${u_1} =  - 50$$ m
For second object,
$${v_2} =  + {{50} \over 7}$$ m, $$f =  + 10$$ m
$$	herefore$$ $${1 \over {{v_2}}} + {1 \over {{u_2}}} = {1 \over f}$$
$${1 \over {(50/7)}} + {1 \over {{u_2}}} = {1 \over {10}}$$ or $${1 \over {{u_2}}} = {1 \over {10}} - {7 \over {50}}$$ or $${u_2} =  - 25$$ m
Speed of the object $$ = {{25} \over {30}}$$ m s
$$-$$1
$$ = {{25} \over {30}} 	imes {{18} \over 5}$$ km h
$$-$$1
= 3 km h
$$-$$1

Ray Optics

Image of an object approaching a convex mirror of radius of curvature 20 m along its optical axis is observed to move from ${{25} \over 3} m to {{50} \over 7}$ m in 30 s. What is the speed of the object in km per hour?

Choose the correct answer: