A luminous point object O is placed at a distance \( 2R \) from the spherical boundary separating two transparent media of refractive indices \( n_1 \) and \( n_2 \), where \( R \) is the radius of curvature of the spherical surface. If \( n_1 = \frac{3}{2} \), \( n_2 = 3 \), and the image is obtained at a distance from P equal to
- 30 cm in the rarer medium
- 30 cm in the denser medium
- 18 cm in the rarer medium
- 18 cm in the denser medium
The Correct Option is D
Solution and Explanation
The relationship between the object distance \( u \), the image distance \( v \), and the radius of curvature \( R \) is given by the lens formula for spherical boundaries:
\( \frac{n_1}{v} - \frac{n_2}{u} = \frac{n_2 - n_1}{R} \)
Substituting the given values for \( n_1 \), \( n_2 \), and \( R \), we calculate the image distance \( v = 18 \, \text{cm} \) in the denser medium.
This means that the image is formed closer to the spherical surface in the denser medium.
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