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Question
The image of a candle flame placed at a distance of 30 cm from a spherical lens is formed on a screen placed on the other side of the lens at a distance of 60 cm from the optical centre of the lens. Identify the type of lens and calculate its focal length. If the height of the flame is 3 cm, find the height of its image.
Solution
Since the image is formed on the screen, the image is real. A concave lens cannot form a real image. Therefore, the lens is convex.
Focal length of the convex lens, f = ?
Object distance, u = ⇒f=20" role="presentation" style="position: relative;" data-mce-style="position: relative;">⇒f=2030 cm
Image distance, v = +60 cm
Since
`1/v-1/u=1/f`
`therefore1/f=1/60-1/((-30))`
`rArr1/f=1/60+1/30`
`rArr1=((1+2))/60`
`rArr1/f=3/60`
`rArrf=20`
Or
f = +20 cm
The magnification of convex lens, `m=v/u`
`rArrm=60/-30`
`rArrm=-2`
`"Magnification, "m=h_i/h_o`
where
hi = Height of image
ho = Height of object
`thereforem=h_i/3`
`rArrh_i=-2xx3`
`rArrh_i=-6`
Here, negative sign indicates that the image formed is inverted.
Therefore, height of image of candle flame is 6 cm.
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