The focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25 cm in front of it to 50 cm, the magnification of its image changes from to . The ratio is _______. [2010]

Question

The focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25 cm in front of it to 50 cm, the magnification of its image changes from $m_{25}$ to $m_{50}$ . The ratio $\frac{m_{25}}{m_{50}}$ is _______. [2010]

Smart Achievers · Accepted Answer

(6)

When $u = - 25 cm$

$\frac{1}{v} = \frac{1}{f} + \frac{1}{u} = \frac{1}{20} + \frac{1}{- 25} = \frac{1}{100}$ $\Rightarrow v = 100 cm$

$m_{25} = \frac{- v}{u} = \frac{- 100}{- 25} = 4$

When $u = - 50 cm$

$\frac{1}{v} = \frac{1}{f} + \frac{1}{u} = \frac{1}{20} + \frac{1}{- 50} = \frac{3}{100}$ $\Rightarrow v = \frac{100}{3} cm$

$m_{50} = \frac{- v}{u} = \frac{- 1000}{3} \times \frac{- 1}{50} = \frac{2}{3}$

So, $\frac{m_{25}}{m_{50}} = \frac{4}{2 / 3} = 6$

Solution

Q.
The focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25 cm in front of it to 50 cm, the magnification of its image changes from $m_{25}$ to $m_{50}$ . The ratio $\frac{m_{25}}{m_{50}}$ is _______. [2010]

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Solution

Q. The focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25 cm in front of it to 50 cm, the magnification of its image changes from m25 to m50. The ratio m25m50 is _______. [2010]

Ans. (6) When u=-25 cm 1v=1f+1u=120+1-25=1100⇒v=100 cm m25=-vu=-100-25=4 When u=-50 cm 1v=1f+1u=120+1-50=3100⇒v=1003 cm m50=-vu=-10003×-150=23 So, m25m50=42/3=6

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Q.
The focal length of a thin biconvex lens is 20 cm. When an object is moved from a distance of 25 cm in front of it to 50 cm, the magnification of its image changes from $m_{25}$ to $m_{50}$ . The ratio $\frac{m_{25}}{m_{50}}$ is _______. [2010]