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Physics Question 27 – JEE-MAIN 2025

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Two thin convex lenses of focal lengths 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this combination is:

When two lenses are placed coaxially at a certain separation, their combined power is affected by their individual powers and the separation distance.

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Ninja Strategy•Special Case Recognition

Recognize that the separation distance d (10 cm) is equal to the focal length of the second lens f2 (10 cm). In this special case, the combined power Pcomb simplifies to P2, which is 1/f2=1/(0.1 m)=10 D.

Step 1: Identify Given Parameters and Convert Units✦ Active

The focal lengths of the two convex lenses are f1=30 cm and f2=10 cm. The separation distance between them is d=10 cm. For power calculations in Diopters, all lengths must be converted to meters.

f1=30 cm=0.3 m  (For convex lenses, focal length is positive)   f2=10 cm=0.1 m  (For convex lenses, focal length is positive)   d=10 cm=0.1 m
Step 2: Apply the Formula for Combined Power○ Expand

The power of a combination of two thin lenses with individual powers P1 and P2, separated by a distance d, is given by the formula Pcomb=P1+P2−dP1P2. First, calculate the individual powers P1=1/f1 and P2=1/f2.

P1=1f1=10.3 m=103 D   P2=1f2=10.1 m=10 D   Pcomb=P1+P2−dP1P2   Pcomb=103+10−(0.1)(103)(10)
💡 Teacher's Secret Hint

Remember to use meters for distance 'd' when calculating combined power in Diopters.

Step 3: Calculate the Combined Power○ Expand

Perform the arithmetic to find the combined power. Notice that the separation distance d is equal to the focal length of the second lens f2 (0.1 m). This simplifies the calculation significantly.

Pcomb=103+10−10030   Pcomb=103+10−103   Pcomb=10 D
💡 Teacher's Secret Hint

A useful shortcut: if d=f2, then Pcomb=P2. If d=f1, then Pcomb=P1.

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