Physics · Reflection of light, spherical mirrors, mirror formula
A point object is placed at a distance and its real image is formed at a distanc
A point object is placed at a distance \( 10 c m \) and its real image is formed at a distance of \( 20 \mathrm{cm} \) from concave mirror If the object is moved by \( 0.1 \mathrm{cm} \) towards the mirror, the image will shift by about
- A. \( 0.4 \mathrm{cm} \) away from the mirror
- B. \( 0.4 \mathrm{cm} \) towards the mirror
- C. \( 0.8 c m \) away from the mirror
- D. \( 0.8 \mathrm{cm} \) towards the mirror
Step-by-step solution
Using the mirror formula 1/v + 1/u = 1/f, with initial u = -10 cm and v = -20 cm, we find f = -20/3 cm. Differentiating gives dv = -(v^2/u^2) du. With du = +0.1 cm (object moves toward mirror, u becomes less negative), v^2/u^2 = 4, so dv = -0.4 cm. Since v is negative, a decrease of 0.4 cm means the image distance magnitude increases by 0.4 cm, shifting the image away from the mirror.
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