Question

An object is situated 40 cm from a convex
mirror: when a plane mirror is inserted between
the object and convex | mirror at a distance
Of 32cm from the object, the image in two mirrors coincide . What is the focal lenght of
convex mirror ?
​

Answer 1

Answer:

u=v for plane mirror =40 cm

v=20 cm for convex mirror as well since the images coincide and distance between the two mirrors is 20 cm.

u for convex mirror =−60 cm (since it is left of the mirror)

From lens formula, f/1

= u/1 + v/1

=− 60/1 + 20/1

f/ 1

= 60/2

f=30cm

Answer 2

Given: An object is situated $40$cm. from a convex mirror. and a plane mirror is at a distance of $32$cm. from the object.

We have to find the focal length of a convex mirror.

The given problem is solved in the following way,

As we know that an object is situated $40$cm. from a convex mirror therefore $U=-40cm.$

And the plane mirror at a distance  of $32$cm. and the image of two mirrors coincide therefore the image will also reflect at the same distance from the plane mirror i.e. $32cm.$

We know that,

$=>\frac{1}{V} +\frac{1}{U} =\frac{1}{F} \\\\=>\frac{1}{24} -\frac{1}{40} =\frac{1}{F} \\\\=>\frac{1}{F} =\frac{1}{60}$

Hence, The focal length of a convex mirror is  is $60cm.$

The following figure will help you to understand briefly,