Question

Combination of lenses are arranged in case I and case II as shown in the figure. In case I, \( f_1 = 5 \, \text{cm} \), and in case II, \( f_2 = 4 \, \text{cm} \), the object is at \( -10 \, \text{cm} \). Magnification in two cases are \( m_1 \) and \( m_2 \). Find \( \left| \frac{m_1}{m_2} \right| \).

• A. \( \frac{5}{6} \)
• B. \( \frac{4}{3} \)
• C. \( \frac{3}{4} \)
• D. \( \frac{6}{5} \)

Hint:

When working with lenses, use the lens formula to find the image distance, and then calculate the magnification.

Answer 1

The Correct Option is A

Step 1: Magnification formula.
Magnification \( m \) for a lens is given by the formula: \[ m = \frac{v}{u} \] where \( v \) is the image distance and \( u \) is the object distance. Using the lens formula: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Step 2: Apply the lens formula for both cases.
For case I: \[ \frac{1}{f_1} = \frac{1}{v_1} - \frac{1}{u_1} \] For case II: \[ \frac{1}{f_2} = \frac{1}{v_2} - \frac{1}{u_2} \] By solving these equations, we can find \( m_1 \) and \( m_2 \). The ratio \( \left| \frac{m_1}{m_2} \right| \) comes out to be \( \frac{5}{6} \). Final Answer: \[ \boxed{\frac{5}{6}} \]