Question

A convex lens forms a real image \(4\,\text{cm}\) long on a screen. When the lens is shifted to a new position without disturbing the object, again a real image is formed on the screen which is \(16\,\text{cm}\) tall. The length of the object must be

• A. \(4\,\text{cm}\)
• B. \(8\,\text{cm}\)
• C. \(12\,\text{cm}\)
• D. \(20\,\text{cm}\) \bigskip

Hint:

In the lens displacement method, \[ m_1=\frac{v_1}{u_1}, \qquad m_2=\frac{v_2}{u_2}, \] and the two magnifications satisfy \[ m_1m_2=1. \] Hence, \[ \left(\frac{h_{i1}}{h_o}\right) \left(\frac{h_{i2}}{h_o}\right)=1. \] This provides a quick way to determine the object height.

Answer 1

The Correct Option is B

Concept: In the displacement method, magnifications for the two positions are reciprocals: \(m_1 m_2 = 1\).

Step 1: \(m_1 = 4/h\), \(m_2 = 16/h\). \((4/h)(16/h) = 1 \Rightarrow 64/h^2 = 1 \Rightarrow h = 8\) cm.

Step 2: Write the final answer. \(\boxed{h=8\,\text{cm}}\)