wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A man is 180 cm tall and his eyes are 10 cm below the top of his head. In order to see this entire height right from toe to head, he uses a plane mirror kept at a distance of 1 m from him. The minimum length of the plane mirror is

A
180 cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
90 cm
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
85 cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
170 cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 90 cm
Total height of man (H)=180 cm
(Including eyes)
Distance between head and eyes,
HE=10 cm
Distance between feet and eyes,
FE=170 cm


Considering man as an extended object in front of mirror, man will be able to see his entire image when the light incident on mirror from his head and feet reaches his eyes after reflection.

From the symmetry of incident and reflected rays(i=r)
HM=EM & EP=PF

At points M & P of mirror, MO and PD will be the perpendicular bisectors of length HE and EF respectively.
NP=ED=EF2
and, MN=OE=EH2
Minimum required length of mirror will be,
Lmin=NP+MN
Lmin=EF2+EH2
Lmin=1702+102=90 cm
Hence, option (b) is the correct answer.

Alternate:
Minimum length of the plane mirror =Height of the man2=1802=90 cm
Key Point: Minimum length of the plane mirror is half the height of the man standing in front of it.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon