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If a convex lens of focal length 10 cm a...

If a convex lens of focal length 10 cm and a concave lens of focal length 50 cm are kept in contact with each other , (i) what will be the focal length of the combination ? (ii) What will be the power of the combination? (iii) What will be the behaviour of the combination ( behaviour as a convex lens / concave lens ) ?

Text Solution

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` f_(2) = - 50 cm` = - 0.5 m ( concave lens ) , f ( combination ) = ?
P ( combination ) = ?
(i) ` 1/f = 1/f_(1) + 1/f_(2) = 1/( 0.1 m) + 1/( - 0.5 m) = 10/m - 2/m = 8/m`
` f = 1/8 m = `0.125 m = 12.5 cm
The focal length of the combination of the lenses = 0.125 m = 12.5 cm.
(ii) ` P _(1) = 1/f_(1) = 1/(0.1 m) = 10 D, P_(2) = 1/f_(2) = 1/(-0.5 m) = -2 D `
` therefore P = P_(1) + P_(2) = 10 D - 2D = 8 D `
` P = 1/f = 1/( 0.125 m) = 8 D `
The power of the combination of the lenses = 8 D
(iii) The focal length of the combination of the lenses is positive. This shows that the combination will behave as a convex lens.
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