Two thin convex lenses of focal lengths 4 cm and 8 cm are separated by a distance of 4 cm in air. The combination will have the focal length

The correct answer is Option 1. When two thin lenses of focal lengths f₁ and f₂ are separated by a distance d, the effective focal length (F) of the combination is calculated using the formula:

1/F = 1/f₁ + 1/f₂ - d/(f₁f₂)

Given the values:

• f₁ = 4 cm
• f₂ = 8 cm
• d = 4 cm

Substituting these into the formula:

1/F = 1/4 + 1/8 - 4/(4 × 8)
1/F = 1/4 + 1/8 - 4/32
1/F = 1/4 + 1/8 - 1/8

The terms +1/8 and -1/8 cancel each other out, leaving 1/F = 1/4. Therefore, the effective focal length F = 4 cm. Options 2, 3, and 4 are incorrect as they do not account for the subtractive effect of the separation distance on the combined power of the lenses.