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 location of the image of A can be found using the lens formula: \[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \] where \( f = 20 \, \text{cm} \), \( u = -30 \, \text{cm} \), and \( v = 60 \, \text{cm} \). Using the magnification formula: \[ m = \frac{v}{u} = \frac{60}{-30} = -2 \] Since the object size is small with respect to the location, we can calculate the small change \( dv \) in the image: \[ dv = m^2 du = 4 \times 1 = 4 \, \text{cm} \] This gives us the size of the image at \( P \) as \( h_i = m h_o = 2 \times 2 = 4 \, \text{cm} \). 
The angle made by the image with the principal axis is \( -45^\circ \), which corresponds to the correct answer.