Question

A slanted object AB is placed on one side of convex lens as shown in the diagram. The image is formed on the opposite side. Angle made by the image with principal axis is:

• A. \( \frac{-\alpha}{2} \)
• B. \( -45^\circ \)
• C. \( +45^\circ \)
• D. \( -\alpha \)

Hint:

When the object is slanted and small compared to the location, use magnification and lens formulas to find the angle made by the image.

Answer 1

The Correct Option is B

The image location for object A is determined via the lens formula: \[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \] with \( f = 20 \, \text{cm} \), \( u = -30 \, \text{cm} \), and \( v = 60 \, \text{cm} \). The magnification is calculated using: \[ m = \frac{v}{u} = \frac{60}{-30} = -2 \] For a small object relative to its position, the image size change \( dv \) can be computed as: \[ dv = m^2 du = 4 \times 1 = 4 \, \text{cm} \] Consequently, the image size at \( P \) is \( h_i = m h_o = 2 \times 2 = 4 \, \text{cm} \).
The image's angle with the principal axis is \( -45^\circ \), aligning with the expected outcome.