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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. - Science

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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.

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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.

Concept: Magnification Due to Spherical Lenses
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