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# The Power of a Combination of Two Lenses X And Y Is 5 D. If the Focal Length of Lens X Be 15 Cm : (A) Calculate the Focal Length of Lens Y. (B) State the Nature of Lens Y. - CBSE (Science) Class 12 - Physics

ConceptRefraction at Spherical Surfaces and by Lenses Power of a Lens

#### Question

The power of a combination of two lenses X and Y is 5 D. If the focal length of lens X be 15 cm :
(a) calculate the focal length of lens Y.
(b) state the nature of lens Y.

#### Solution

(a) The focal length of lens X, ie., f1 = 15 cm = 0.15 m
Power of lens X, p_-1=1/f_1=1/0.15=6.67 D
Let the power and the focal length of the lens Y be P2 and f2respectively.
The resultant power of the combination of two lenses is the algebraic sum of the powers of the individual lenses.
∴ Power of combination of lenses P = P1 + P2
⇒5 = 6.67 + P2
​                               ⇒P2 = 5 - 6.67 = - 1.67 D
The power of the lens is related to the focal length of the lens as:

p_2=1/f_2

-1.67=1/f_2

f_2=1/-1.67=0.60m=-60cm

f_2=1/-1.67=-0.60m=-60cm

The focal length of the lens Y is -60 cm.

(b) The focal length of the lens Y is negative. Therefore, the lens is concave and diverging in nature.

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Solution The Power of a Combination of Two Lenses X And Y Is 5 D. If the Focal Length of Lens X Be 15 Cm : (A) Calculate the Focal Length of Lens Y. (B) State the Nature of Lens Y. Concept: Refraction at Spherical Surfaces and by Lenses - Power of a Lens.
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