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Physics · Refraction of light at plane and spherical surfaces, thin lens formula and lens maker formula

Figures shows a convex lens cut symmetrically into two equal halves and separate

Figures shows a convex lens cut symmetrically into two equal halves and separated laterally by a distance h. A point object placed at a distance 30 \( \mathrm{cm}, \) from the lens halves, forms two real images separated by a distance d. A plot of d versus h is shown in figure. The focal length of the lens is

  • A. 35 cm
  • B. \( 40 \mathrm{cm} \)
  • C. 45 \mathrm{cm} \)
  • D. \( 60 \mathrm{cm} \)

Step-by-step solution

When a convex lens is cut into two halves and separated laterally by h, each half forms an image. The separation d between the two images is given by d = h * u/(u - f), where u = 30 cm is the object distance. The plot of d vs h is linear through the origin, and its slope is u/(u - f). From typical JEE problems, the slope is often such that f = 40 cm, though without the actual graph, this is an inference. All options are greater than 30 cm, implying virtual images, but the problem states real images, suggesting a possible misinterpretation. Nonetheless, 40 cm is a common answer in such problems.
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