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

In the figure shown radius of curvature of either surface of equi convex half lens is 40 cm and refractive index 1.5. Its one side is silvered. A plane mirror is also placed. A small object O is placed such that there is no parallax between final image formed by lens and mirror. If transverse length of final image formed by silvered lens system is twice that formed by mirror. Choose the correct options:


A
a=2.5 cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
b=5 cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
Distance of image from object is 15 cm
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
Image formed by silvered lens system is virtual
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D Image formed by silvered lens system is virtual

Distance of object from the plane mirror AB=a+b
Image will be formed by the plane mirror at a distance of (a+b) behind the mirror.
From the above statement we can say that the polished lens will also form image at the same place.
Distance of image from combination is therefore gievn by :-
OC=b+(a+b)
OC=a+2b
Now, according to the question m=2 for the polished lens.
OCAO=2
a+2ba=2
or, a=2b ..(1)
Now, we can say that the focal length of the polished lens can be calculated by incidenting a parallel beam of light on the combination of the lens and concave mirror. Since, in this process refraction from the lens takes place 2 times. So, from the formula of power of combination of lens and mirror we can say that, focal length of combination.
1F=1fm1fl1fl
or, 1F=1fm2fl
Here, fl is given by :-
1fl=(1.51)(140140)
fl=40 cm
and fm=20 cm
1F=120240
1F=440
F=10 cm
Now, applying mirrors formula for the combination since, the combination is behaving as a concave mirror of focal length 10 cm
1F=1v+1u
1F=1OC+1OA
110=1(2b+a)+1a
110=12a1a
[a=2b]
a=5 cm
and b=2.5 cm
Distance of image from the object
=AC
=2(a+b)=2×(5+2.5)
=15 cm
Imaged formed by silvered lens system is virtual.

flag
Suggest Corrections
thumbs-up
1
similar_icon
Similar questions
View More
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Thin Lenses: Extended Objects
PHYSICS
Watch in App
Join BYJU'S Learning Program
CrossIcon