A combination of lenses for a camera contains two converging lenses of focal lengths 20 cm and 40 cm and a diverging lens of focal length 50 cm. Find the power and focal length of the combination.A optical instrument in which the above arrangement of convex lens is used is a convex lens used to burn paper by focusing sunlight.
Solution
Focal length (f1) of the 1st converging lens = 20 cm = 0.2 m
Focal length (f2) of the 2nd converging lens = 40 cm = 0.4 m
Focal length (f3) of the diverging lens = -50 cm = -0.5 m (negative sign due to sign convention)
Power = `1/"foccal length of lens (in metre)"`
Power (P1) of 1st lens = `1/0.2=2.5D`
power (P2) of 2nd lens = `1/0.4=2.5 D`
Power (P3) of diverging lens =`1/0.5 =-2D`
Net power of the combination = P1 + P2+ P3 = 5 + 2.5 + (-2) = 5.5 D
Net focal length of the combination = `1/"net power"=1/5.5=0.1818m=18.18 cm`
