In the figure shown M₁ and M₂ are two spherical mirrors of focal length 20cm each. AB and CD are their principal axes respectively. Which are separated by 1cm. PQ is an object of height 2cm and kept at distance 30cm from M₁. The separation between the mirrors is 50cm. Consider two successive reflections first on M₁ then on M₂. Find the size of the 2nd image (in cm)
Physics · Mixed Chapter
JEE Mains

Question

In the figure shown M₁ and M₂ are two spherical mirrors of focal length 20cm each. AB and CD are their principal axes respectively. Which are separated by 1cm. PQ is an object of height 2cm and kept at distance 30cm from M₁. The separation between the mirrors is 50cm. Consider two successive reflections first on M₁ then on M₂. Find the size of the 2nd image (in cm)

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1: The first mirror M₁ has |f₁|=20 cm and object distance 30 cm. Mirror formula in magnitudes for this concave reflection gives image distance v₁=(20×30)/(30−20)=60 cm. Step 2: Magnification magnitude for M₁ is |m₁|=60/30=2, so the first image is 4 cm tall. Step 3: M₂ is 50 cm from M₁. The converging rays would meet 60−50=10 cm behind M₂; this is a virtual object for the second reflection. With the mirror orientation shown and |f₂|=20 cm, the second image distance magnitude is 20 cm. Step…