A point object is placed at a distance of 0.3 m from a convex lens (focal length 0.2 m) cut into two halves each of which is displaced by 0.0005 m as shown in the figure. Find the position of the image . If more than one image is formed find their number and the distance between them.

Options

A. 0.1cm
B. 0.5cm
C. 0.3cm
D. 1cm

Answer

c.

Explanation

Each half lens will form an image in the same plane. The optic axes of the lenses are displaced,
`(1)/(upsilon)-(1)/((-30))=(1)/(20),upsilon=60cm`
From similar triangle `OI_(1)I_(2)` and `OP_(1)P_(2)` , we have
`(I_(1)I_(2))/(P_(1)P_(2))=(u+upsilon)/(u)I_(1)I_(2)=(90)/(30)(2xx0.05)=0.3cm`
Thus, the two images are 0.3cm apart. Alternatively, imagine two arrows(see figure) that act as objects for the lens.
Magnification, `m=(upsilon)/(u)=((+60))/((-30))=-2`
Image of height of arrow is `y=2xx(0.005)=0.10cm`
Thus, two inverted images are formed whose tips are at `I_(1)` and `I_(2)` respectively.
Thus, `I_(1)I_(2)=2y+Delta=(2xx0.01)+0.1=0.3cm`