Question

An objest is placed in front of a convex mirror at the distance of 50 cm a plane mirror is introduced converging the lower half of the convex mirror if the distance between the object and the plane mirror is 30 cm It is found that there is no parallel axis between the images formed by the two Mirrors radius of curvature of convex mirror will be ​

Answer 1

Answer :-

$\sf{\red{Option\:(2)}\:25\:cm}$

$\rule{200}2$

Explanation :-

[ Refer the attachment for figure ]

An object is placed 50 cm from a convex mirror. Also, a plane mirror is introduced before the converging mirror. And the distance between the plane mirror and the object is 30 cm.

Now,

Distance between plane mirror and object is (50 - 30) cm = 20 cm

Also,

A plane mirror is 30 cm away from the convex mirror. And we know that image formed by a plane mirror is at same distance; at which distance its object is placed.

Means, the distance between the plane mirror and the object is 30 cm. So, the distance between the plane mirror and the image is also 30 cm.

So, image distance = 30 - 20 = 10 cm

As, there is convex mirror also, which is placed 20 cm apart from plane mirror.

$\implies$ v = image distance = + 10 cm

$\implies$ u = object distance = - 50 cm

Now,

According to mirror formula

1/f = 1/v + 1/u

⇒ 1/f = 1/10 + 1/(-50)

⇒ 1/f = 1/10 - 1/50

⇒ 1/f = (5 - 1)/50

⇒ 1/f = 4/50

⇒ f = 50/4

⇒ f = 12.5 cm

Now,

R = 2f

⇒ R = 2(12.5)

⇒ R = 25 cm

Answer 2

Given :----

• object is in front of convex mirror at a distance of 50cm.
• distance b/w object and plane mirro = 30cm .

To Find :---

• Radius of curvature of convex mirror.

Formula used :----

• 1/f = 1/v + 1/u
• R = 2F

Solution :-----

[ Refer to image first ]

→ The plane mirror and the convex mirror both form the image at the same position.

Given , object distance = 30cm (From plane mirror)

The plane mirror will form erect and virtual image of same size at a distance of 30cm behind it.

so, image distance = 30cm (Behind the mirror)

So, the distance of image formed by plane mirror from convex mirror will be = 30 - 20 = 10cm (Behind the convex mirror)

Now,

For convex Mirror ,

u = -50cm

v = 10cm

Putting values in mirror formula we get,

1/f = 1/10 + 1/(-50)

→ 1/f = 1/10 - 1/50

→ 1/f =(5-1) /50

→ 1/f = 4/50

→ 1/f = 1/12.5

→ f = 12.5cm .

Now,

Radius of curvature of convex mirror = 2×f = 2×12.5 = 25cm(2 option)

(Hope it helps you)