COMEDK Exam 2018 Solved Paper

Let f1 and f2 are focal lengths of convex and concave lens respectively, when they are kept in contact co-axially, then focal length F of the combination is given as
‌

1

F

‌=‌

1

f1

+‌

1

(−f2)

‌‌[

‌ Focal length of concave ‌

‌ lens is negative. ‌

]
⇒‌‌‌

1

F

‌=‌

f2−f1

f1f2

⇒‌‌F‌=‌

f1f2

f2−f1

. . . (i)
When both lenses are kept at a distance d, then their combined focal length F′ is given as
‌

1

F′

‌=‌

1

f1

+‌

1

(−f2)

−‌

d

f1(−f2)

⇒‌‌‌

1

F′

‌=‌

1

f1

−‌

1

f2

+‌

d

f1f2

⇒‌‌‌

1

F′

‌=‌

f2−f1+d

f1f2

⇒‌‌F′‌=‌

f1f2

f2−f1+d

. . . (ii)
From Eqs. (i) and (ii), it is clear that F′<F i.e. focal length of combination will decrease.