Question

The distance between an object and the screen is $100 \, cm.$ A lens produces an image on the screen when placed at either of two positions $40 \, cm$ apart. The power of the lens is approximately

• A. $3 \, D$
• B. $5 \, D$
• C. $7 \, D$
• D. $9 \, D$

Answer 1

Answer: (B)

Given, $D=100 \, cm, \, x=40 \, cm$
$\therefore f = \frac{D^{2} - x^{2}}{4 \, \, \text{D}}$
If $a$ be his maximum upward acceleration, then $\left(70 \, kg\right)g=\left(60 \, kg\right)g+\left(60 \, kg\right)a$
$\therefore \, \, a=\frac{\left(70 \, kg\right) g - \left(60 kg\right) g}{60 \, kg}$
$=\frac{g}{6}=\frac{9.8 \, m s^{- 2}}{6}=1.63ms^{- 2}$
$f=\frac{\left(100\right)^{2} - \left(40\right)^{2}}{4 \times 100}$
$=\frac{\left(100 + 40\right) \, \left(100 - 40\right)}{400}$
$=\frac{140 \times 60}{400}=21 \, cm$
We know that $P=\frac{100}{f \left(c m\right)}=\frac{100}{21}=5 \, D$