A convex lens has a focal length of 20 cm. At what distance from the lens should a candle be placed so that its real and inverted image is formed at a distance of 60 cm from the lens? Also, find the magnification.

Q: A convex lens has a focal length of 20 cm. At what distance from the lens should a candle be placed so that its real and inverted image is formed at a distance of 60 cm from the lens? Also, find the magnification.

Given:\nFocal length of convex lens ($f$) = $+20$ cm\nImage distance ($v$) = $+60$ cm (real image is formed on the other side)\nObject distance ($u$) = ?\nMagnification ($m$) = ? \nUsing the lens formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ \nRearranging for $u$: $\frac{1}{u} = \frac{1}{v} - \frac{1}{f}$ \nSubstitute the values: $\frac{1}{u} = \frac{1}{60} - \frac{1}{20}$ $\frac{1}{u} = \frac{1 - 3}{60}$ $\frac{1}{u} = \frac{-2}{60} = -\frac{1}{30}$ $u = -30$ cm \nThe candle should be placed at a distance of 30 cm in front of the convex lens. \nNow, calculating the magnification ($m$): $m = \frac{v}{u}$ $m = \frac{+60}{-30} = -2$ \nThe negative sign indicates that the image formed is real and inverted, and its size is twice the size of the candle.

Question

Accepted Answer

Given:
Focal length of convex lens ($f$) = $+20$ cm
Image distance ($v$) = $+60$ cm (real image is formed on the other side)
Object distance ($u$) = ?
Magnification ($m$) = ? 
Using the lens formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ 
Rearranging for $u$: $\frac{1}{u} = \frac{1}{v} - \frac{1}{f}$ 
Substitute the values: $\frac{1}{u} = \frac{1}{60} - \frac{1}{20}$ $\frac{1}{u} = \frac{1 - 3}{60}$ $\frac{1}{u} = \frac{-2}{60} = -\frac{1}{30}$ $u = -30$ cm 
The candle should be placed at a distance of 30 cm in front of the convex lens. 
Now, calculating the magnification ($m$): $m = \frac{v}{u}$ $m = \frac{+60}{-30} = -2$ 
The negative sign indicates that the image formed is real and inverted, and its size is twice the size of the candle.

MP Board · Class 10 · Science · Light – Reflection and RefractionA convex lens has a focal length of 20 cm. At what distance from the lens should a candle be placed so that its real and inverted image is formed at a distance of 60 cm from the lens? Also, find the magnification.