Question

An object is located in a fixed position in front of a screen. Sharp image is obtained on the screen for two positions of a thin lens separated by 10 cm. The size of the images in two situations are in the ratio 3 : 2. What is the distance between the screen and the object

• A. 65.0 cm
• B. 99.0 cm
• C. 144.5 cm
• D. 124.5 cm

Answer 1

Answer: (B)

99.0 cm

1st position $u=-x,v=+y$

$m_1=\frac{v}{u}=\frac{+y}{-x}$

2nd position $u=-y,v=+x$

$m_2=\frac{v}{u}=\frac{+x}{-y}$

Also, $\frac{m_1}{m_2}=\frac{3}{2}$........(given)

$y=\sqrt{\frac{3}{2}}x$

$y-x=10$

By Solving these above equations, we get

$y=44.5,x=54.5$

So, $d=x+y=99cm$