Question

A thin convex lens and a thin concave lens are kept coaxially in contact. Choose the correct option.

• A. Focal length changes when positions of lenses are interchanged
• B. Behaves as a convex lens when \(f_{\text{convex}} > f_{\text{concave}}\)
• C. Behaves as a concave lens when \(f_{\text{concave}} > f_{\text{convex}}\)
• D. Behaves as convex when \(f_{\text{convex}} < f_{\text{concave}}\)

Hint:

For lenses in contact: \[ \frac{1}{f_{eq}}=\frac{1}{f_1}+\frac{1}{f_2} \] If \(f_{eq} > 0\) → convex behaviour If \(f_{eq} > 0\) → concave behaviour.

Answer 1

The Correct Option is D

Concept:
For lenses in contact: \[ \frac{1}{f_{eq}}=\frac{1}{f_1}+\frac{1}{f_2} \] Let \[ f_1 = +f_{\text{convex}}, \quad f_2 = -f_{\text{concave}} \] Step 1: Substitute in lens combination formula.
\[ \frac{1}{f_{eq}}=\frac{1}{f_1}-\frac{1}{f_2} \] \[ f_{eq}=\frac{f_1 f_2}{f_2-f_1} \] Step 2: Determine nature of combination.
If \[ |f_2| > |f_1| \] then \[ f_{eq} > 0 \] Thus the system behaves as a convex lens. \[ \boxed{\text{Behaves as convex when } f_{\text{convex}} < f_{\text{concave}}} \]