CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A plane mirror is placed at a distance of 50 cm from a concave mirror of focal length 16 cm. Where should a short object be placed between the mirrors and facing both the mirrors so that its virtual image in the plane mirror coincides with the real image in concave mirror?

A
30 cm from the concave mirror
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
20 cm from the plane mirror
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
15 cm from the concave mirror
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
30 cm from the plane mirror
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D 30 cm from the plane mirror
Let the distance between object AB and plane mirror is x cm.

distance between object AB and concave mirror is (50x) cm

So, from the above diagram,

AM=AM=x

Image formed in the plane mirror will be at a distance x from plane mirror towards right and thus (50+x) from concave mirror.

OA=OM+AM=(50+x) cm

For concave mirror:

Object distance for concave mirror, u=(50x)
Image distance for concave mirror, v=(50+x)
And, focal length, f=16 cm

Applying mirror formula,

1v+1u=1f

1(50+x)+1(50x)=116

50x+50+x502x2=116

100×16 = 2500 x2

x=30 cm

Hence correct option is (d).

flag
Suggest Corrections
thumbs-up
5
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon