Question

1.
An object O is placed in front of a small plane mirror M, and a large convex mirror
M, of focal length f. The distance between 0 and M is x, and the distance between
M, and M is y. The images of O formed by M, and M, coincide. Find the focal
length of the mirror.
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Answer 1

Answer:

An object O is placed in front of a small plane mirror=M

1

and a large convex mirror=M

2

of focal length=f

The distance between O and M

1

is =x

u=x+y and

v=x−y

Using mirror formula,

f

1

=

v

1

−

u

1

f

1

=

x+y

1

−

x−y

1

f

1

=

x+y

1

−

x−y

1

=

(x+y)(x−y)

x−y−x−y

=

x

2

−y

2

2y

f=

2y

x

2

−y

2