Question

A beam of light parallel to the principal axis of a concave and convex lens, first passes through the concave lens of focal length \( 0.5 \, \text{m} \) and then through the convex lens of focal length \( 1.75 \, \text{m} \). If the lenses are placed \( 1.25 \, \text{m} \) apart, which of the given statement is true?

• A. The emergent beam will focus at \( 1.75 \, \text{m} \) on the principal axis.
• B. The emergent beam will focus at \( 1.25 \, \text{m} \) on the principal axis.
• C. The emergent beam will pass parallel to the principal axis.
• D. The emergent beam will focus at \( 0.75 \, \text{m} \) on the principal axis.

Hint:

If the object for a convex lens is at its focus, the emergent rays become parallel to the principal axis.

Answer 1

The Correct Option is C

Step 1: Identify the nature of first lens.
The first lens is a concave lens, so its focal length is negative:
\[ f_1 = -0.5 \, \text{m} \]

Step 2: Understand effect of concave lens.
A parallel beam after passing through a concave lens appears to diverge from its focus.

Step 3: Locate the virtual image formed by concave lens.
The virtual image is formed at the focus of the concave lens, i.e. \( 0.5 \, \text{m} \) before the concave lens.

Step 4: Find object distance for convex lens.
The distance between the two lenses is \( 1.25 \, \text{m} \). So, for the convex lens, the virtual object distance is:
\[ 1.25 + 0.5 = 1.75 \, \text{m} \]

Step 5: Compare with focal length of convex lens.
The focal length of the convex lens is:
\[ f_2 = 1.75 \, \text{m} \] Thus, the virtual object for the convex lens lies at its focus.

Step 6: Use lens property.
When rays appear to come from the focus of a convex lens, after refraction through the convex lens, they emerge parallel to the principal axis.

Step 7: Final Answer.
Hence, the emergent beam will pass parallel to the principal axis.
\[ \boxed{\text{The emergent beam will pass parallel to the principal axis.}} \]