A convex lens made of glass (\( \mu = 1.5 \)) has both radii of curvature 20 cm each. A point object is placed on the principal axis at a distance of 40 cm from the lens. The distance of the image from the lens is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 40 cm
First find the focal length with the lens maker's formula, then use the lens formula. Sign convention: distances measured from the lens, positive along the direction of the incident light. For a double convex lens \( R_1 = +20\,\mathrm{cm} \) and \( R_2 = -20\,\mathrm{cm} \).
\( \displaystyle \frac{1}{f} = (\mu - 1)\left(\frac{1}{R_1} - \frac{1}{R_2}\right) \)
\( \displaystyle \frac{1}{f} = (1.5 - 1)\left(\frac{1}{20} + \frac{1}{20}\right) = \frac{1}{20}\,\mathrm{cm^{-1}} \)
\( f = +20\,\mathrm{cm} \)
The object is at \( u = -40\,\mathrm{cm} \).
\( \displaystyle \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \)
\( \displaystyle \frac{1}{v} = \frac{1}{20} + \frac{1}{-40} = \frac{2 - 1}{40} = \frac{1}{40} \)
\( v = +40\,\mathrm{cm} \)
Shortcut: For \( \mu = 1.5 \) an equiconvex lens has \( f = R \). Here \( f = 20\,\mathrm{cm} \) and the object is at 40 cm, that is at \( 2f \). An object at \( 2f \) always forms its image at \( 2f \) on the other side, so \( v = 40\,\mathrm{cm} \) with no calculation.