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Acids, Bases And Salts

Question
CBSEENSC10014622

The image of a candle flame placed at a distance 30 cm from a spherical lens is formed on a screen placed at a distance of 60 cm from the lens. Identify the type of lens and calculate its focal length. If the height of the flame is 2.4 cm, find the height of its image.

Solution

Given,

Object distance, u = − 30 cm

Image distance, v = 60 cm

Height of the object, h = 2.4 cm

Using lens formula,

 
1 over straight f space equals 1 over straight v minus 1 over straight u

1 over straight f space equals 1 over 60 minus fraction numerator 1 over denominator negative 30 end fraction
equals 1 over 60 plus 1 over 30
equals fraction numerator 1 plus 2 over denominator 60 end fraction
equals 3 over 60 equals 1 over 20

straight f equals plus 20 space cm

Since comma space the space focal space length space is space positive comma space the space lens space is space convex space lens.

Now comma
Magnification comma space straight m equals space straight v over straight u equals straight h to the power of apostrophe over straight h

equals space fraction numerator 60 over denominator negative 30 end fraction equals fraction numerator straight h apostrophe over denominator 4 end fraction
straight h apostrophe space equals negative 4.8 space cm space is space the space required space height space of space the space image