Question

An object starts moving at an angle of $45$ with the principal axis as shown in fig. 1.445 in the front of a biconvex lens of focal lenth +10cm if $\theta$ denotes the angle at which image starts to move with principal axis , then

• A. $\theta$=$\frac{3\pi }{4}$
• B. $\theta$=$\frac{\pi }{2}$
• C. $\theta$=$\frac{\pi }{4}$
• D. $\theta$=$\frac{\pi }{6}$

Answer 1

The correct option is A $\theta$=$\frac{3\pi }{4}$

Angle made by the object with X-axis = ${45}^{\circ }$

Distance of the object (v) = 20 cm

Focal length (f)= 10 cm

It can be observed that v = 2f. That is the object is placed at the radius of curvature of the biconvex lens. So the image will also be formed at a distance of 20 cm from the lens and the image will be inverted.

As the image is inverted, transverse magnification will be -1 and lateral magnification will be the same

Angle made by the image $\left(\theta \right)$ = $2\pi -\frac{\pi }{4}$

$\Rightarrow \theta =\frac{\pi }{4}$

The image starts to move at an angle of $\frac{3\pi }{4}$ with the principal axis