Question

a convex lens of focal length 40 cm and a concave lens of focal lenght 50 cm are placed in contact with each other.(i) calculate the power of lens (ii) the focal lenght of the lens combination

Answer 1

convex lens f = +40 cm  as the principal focal point is in the direction of the rays.
concave lens = -50 cm as the principal focal point is on the side of the object.

combination of thin lenses:  1/f = 1/f1 + 1/f2 = 1/40 - 1/50 = 1/200 
    f = 200 cm  positive so convex lens

P1 = 1 /(40/100) meter = 2.5 Dioptre
P2 = 1/(-50/100)m = -2 D 

power of combination = P = P1 + P2 = 2.5 - 2.0 = 0.5 D
                or,  1/(200/100)m   = 1/2 = 0.5 D

Answer 2

convex lens f = +40 cm 
concave lens = -50 cm
combination of thin lenses:
 1/f = 1/f1 + 1/f2 = 1/40 - 1/50 = 1/200 
    f = 200 cm  positive so convex lens
P1 = 1 /(40/100) meter = 2.5 Dioptre
P2 = 1/(-50/100)m = -2 D 
power of combination = P = P1 + P2 = 2.5 - 2.0 = 0.5 D