Physics · Refraction of light at plane and spherical surfaces, thin lens formula and lens maker formula
A needle of length placed from a lens form an image on a screen placed on the ot
A needle of length \( 5 \mathrm{cm}, \) placed \( 45 \mathrm{cm} \) from a lens form an image on a screen placed \( 90 \mathrm{cm} \) on the other side of the lens. The type of lens and its focal length are :
- A. convex, 30 cm
- B. concave, 30 cm
- C. convex, \( 60 \mathrm{cm} \)
- D. concave, 60 cm
Step-by-step solution
The image is formed on a screen, so it is real, which requires a convex lens. Using the lens formula 1/f = 1/v - 1/u with sign convention (u = -45 cm, v = +90 cm), we get 1/f = 1/90 - 1/(-45) = 1/90 + 1/45 = 3/90 = 1/30, so f = 30 cm. Thus, convex lens with focal length 30 cm.
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