Question

3. Three lenses have a combined power of 2.7D. If the powers of two lenses are 2.5D and 1.7D
respectively, find the focal length of the third lens.
(1) 66.66 cm
(2) -6.666 cm
(3) 66.66 m
(4) -6.666 m​

Answer 1

focal length of 3rd lens is - 66.66 cm

if we combine three lens of power P1, P2 and P3 ,

then, effective power, P = P1 + P2 + P3

given, P = 2.7D , P1 = 2.5 D and P2 = 1.7D

so, 2.7 D = 2.5D + 1.7D + P3

⇒2.7D - 1.7D - 2.5D = P3

⇒1 D - 2.5D = P3

⇒P3 = -1.5D

we know power of lens is reciprocal of its focal length.

so, P3 = 1/f3

⇒f3 = 1/P3 = 1/(-1.5D)

= -0.6666 m

= -66.66 cm

hence, option (3) is correct choice.

also read similar questions: Two thin lenses of power +3.5D and -2.5D are placed in contact find the power and focal length of the lens combination?

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Two thin lenses of power +6D and -2D are in contact . What is focal length of the combination

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Answer 2

Focal length of three lenses is - 0.666 m

Explanation:

given,

Combined power of a three lenses , p = 2.7 D

power of two lenses are ,

$p_1$ = 2.5 D

$P_2$ = 1.7 D

$P_3$ = ?

Focal length of three lenses  = ?

accoeding to the question,

$p = p_1 + p_2 +p_3$

put the above values,

$2.7 = 2.5 + 1.7 + p_3$

$p_3 = - 1.5$D

Focal length of three lenses,

$f_3 = \frac{1}{p_3}$

$f_3 = \frac{1}{ - 1.5}$

$f_3 = -0.66 m$