An achromatic doublet is a converging lens of equivalent focal length $100 c m$ . If the dispersive powers of the material of the lenses are in the ratio $1 : 2$ . The focal lengths of the two lenses are:
$- 50 c m, + 100 c m$
$+ 50 c m, - 100 c m$
$- 50 c m, - 100 c m$
$+ 50 c m, + 100 c m$

Question

An achromatic doublet is a converging lens of equivalent focal length $100 c m$ . If the dispersive powers of the material of the lenses are in the ratio $1 : 2$ . The focal lengths of the two lenses are:
$- 50 c m, + 100 c m$
$+ 50 c m, - 100 c m$
$- 50 c m, - 100 c m$
$+ 50 c m, + 100 c m$

Toppr Admin · Accepted Answer

F-100cm- Now- from question- f1-f2-1-2-x27F9-f2-2f1For an achromatic combination-xA0-f1w1-f2w2-0Also- the effective focal length of the combination will be-1f-1f1-1f2Solving these simultaneously and substituting the values-xA0-the obtained focal lengths are- fo-50-xA0-and-xA0-fe-x2212-100

An achromatic doublet is a converging lens of equivalent focal length 100cm. If the dispersive powers of the material of the lenses are in the ratio 1:2. The focal lengths of the two lenses are:−50cm,+100cm+50cm,−100cm−50cm,−100cm+50cm,+100cm

f=100cm, Now, from question: f1:f2=1:2⟹f2=2f1For an achromatic combination, f1w1+f2w2=0Also, the effective focal length of the combination will be,1f=1f1+1f2Solving these simultaneously and substituting the values, the obtained focal lengths are: fo=50 and fe=−100

An achromatic doublet is a converging lens of equivalent focal length $100 c m$ . If the dispersive powers of the material of the lenses are in the ratio $1 : 2$ . The focal lengths of the two lenses are:
$- 50 c m, + 100 c m$
$+ 50 c m, - 100 c m$
$- 50 c m, - 100 c m$
$+ 50 c m, + 100 c m$