Question

A convex lens of focal length 1 meter is placed in contact with another concave lens of equal focal length. What is the focal length of the new lens so formed? (A) infinity (B) +2 m (C) +1 cm (D) None of these. ​

Answer 1

Answer:

$Let \: f_1 \: be \: focal \: length \: of \: convex \: lens = 1 m \\ \\ And \: f_2 \: be \: focal \: length \: of \: concave \: lens = - 1 m \\ \\ Minus \: sign \: because \: focal \: length \: of \: concave \: lens \: is \: always \: negative \\ \\ Using \: formula, \\ \\ \boxed{\frac{1}{F_{combination}} = \frac{1}{f_1} + \frac{1}{f_2}} \\ \\ \frac{1}{F_{combination}} = \frac{1}{f_1} + \frac{1}{f_2} \\ \\ \frac{1}{F_{combination}} = \frac{1}{1} + \frac{1}{-1} \\ \\ \frac{1}{F_{combination}} = 1 - 1 = 0 \\ \\ \huge\boxed{{F_{combination} = \infty }}$

So option (A) is correct