In displacement method, the distance between object and screen is 96cm. The ratio of lengths of two images formed by a converging lens placed between them is 4. Then,

Options

A. Ratio of the length of object to the length of shorter image is 11/5.
B. Distance between the two positions of the lens is 36 cm.
C. Focal length of the lens is 22.5 cm
D. Distance of the lens from the shorter image is 30cm.

Answer

A, B, D

Explanation

For first & second position `(v)/(u)=(I_(1))/(O),(u)/(v)=(I_(2))/(O)`
`rArr (v^(2))/(u^(2))=(I_(1))/(I_(2))=4.84`
`rArr (v)/(u)=2.2` and `v+u =96`
`rArr v=66, u=30`
`(O)/(I_(2))=(v)/(u)=2.2 =(11)/(5)`
`rArr A` is True
Distance between two position of lens `= v-u`
`= 36 cm rArr B` is True
Focal length of lens `f`
`= ("uv")/("u+v")=(66 xx 30)/(66+30)=20.63 rArr C` is False
Distance of lens from shorter image `=u =30 cm rArr D` is True.