what is the focus distance of a combined lens made by combining a concave lens of 25 cm focus distance placed in contact with a convex lens of 20 cm focus distance? whether this combination is convergent lens or divergent?
Answers
Given:-
- Focal length of concave lens f_(1) = - 25 cm
- Focal length of convex lens f_(2) = + 20 cm
To Find :-
- The combination is convergent or divergent lens=?
Solution :-
we will solve this question by applying formula. As given in the question that the focus distance of a combined lens made by combining a concave lens of 25 cm focus distance placed in contact with a convex lens of 20 cm focus distance. Note if combination lens come with negative sign then power of lens be divergent, if combined lens come with positive sign then power of lens be convergent.
Calculation begin :-
- Total focal length of combination lens
➞ 1/f = 1/f_(1) + 1/f_(2)
➞ 1/f = 1/-25 + 1/20
➞ 1/f = -4 + 5/100
➞ 1/f = 1/100
➞ f = 100
- Now calculate power of combination:-
➞ Power (P) = P_(1) + P_(2)
- f_(1) = -25 f_(2) = 20
➞ 1/f ÷ f_(1) = -25/100 = - 0.25
➞ 1/f ÷ f_(2) = 20/100 = 0.20
➞ Power (P) = 1/P_(1) + 1/P_(2)
➞ P = 1/-0.25 + 1/0.20
➞ P = -100/25 + 100/20
➞ P = -400 + 500/100
➞ P = 100/100
➞ P = + 1D
Here we get the power of lens with positive sign so, the combination of lens be convergent:-
Hence,
- The combination is convergent
Answer:
Calculation begin :-
Total focal length of combination lens
➞ 1/f = 1/f_(1) + 1/f_(2)
➞ 1/f = 1/-25 + 1/20
➞ 1/f = -4 + 5/100
➞ 1/f = 1/100
➞ f = 100
Now calculate power of combination:-
➞ Power (P) = P_(1) + P_(2)
f_(1) = -25 f_(2) = 20
➞ 1/f ÷ f_(1) = -25/100 = - 0.25
➞ 1/f ÷ f_(2) = 20/100 = 0.20
➞ Power (P) = 1/P_(1) + 1/P_(2)
➞ P = 1/-0.25 + 1/0.20
➞ P = -100/25 + 100/20
➞ P = -400 + 500/100
➞ P = 100/100
➞ P = + 1D
Here we get the power of lens with positive sign so, the combination of lens be convergent:-
Hence,
The combination is convergent