Question

A convex mirror and a concave mirror of radius 10cm each are placed 15cm apart facing each other. An object is placed midway between them. If the reflection first takes place in the concave mirror and then in convex mirror, the position of the final image is
A. on the pole of the convex mirror
B. on the pole of the concave mirror
C. at a distance of 10cm from the convex mirror
D. at a distance of 5cm from the convex mirror

Answer 1

Hint: The radius of a mirror is its focal length. For concave mirror focal length is considered to be negative. The two lenses are separated by a distance of 15cm and the object is placed just at the middle point which divides the distance between two lenses equally.

Complete answer:
Here ‘O’ is the object, and it is placed halfway between the two mirrors.
We know that for, concave mirror
u$_{1}$ =−7.5 and f$_{1}$ =−5
On applying mirror formulae,

$\dfrac{1}{f{{~}_{1}}}=\dfrac{1}{{{v}_{1}}}+\dfrac{1}{{{u}_{1}}}$
$\implies \dfrac{1}{{{v}_{1}}}-\dfrac{2}{15}=\dfrac{-1}{5}$
v$_{1}$=−15
From the value of v ,we can depict that the image is formed at pole of convex mirror
Now , for the convex mirror ,
u$_{2}$ =0 and f$_{2}$=+5
On applying mirror formulae,
$\implies \dfrac{1}{{{f}_{2}}}=\dfrac{1}{{{v}_{2}}}+\dfrac{1}{{{u}_{2}}}$
$\implies \dfrac{1}{{{v}_{2}}}+\dfrac{1}{0}=\dfrac{1}{5}$
$\implies v_{2}=0$

So the final image is formed at the pole of the convex mirror .

So, the correct answer is “Option A”.

Additional Information:
Snell's law is a formula that is used to describe the relation between the angle of incidence and the angle of refraction, it is referred to light or other waves passing through a boundary between two different mediums.
Angle of incidence is an angle between a ray incident on a surface and the normal.
Angle of refraction is an angle between a refracted ray on a surface and the normal.

Note:
Focal length of a convex mirror is considered as positive whereas of a concave mirror is considered negative, in the mirror formulae f is the focal length v is image distance and u is the object distance from the lens. Students sometimes confuse between object distance and image distance.