A real, inverted image is formed at a distance of 30 cm in front of a concave mirror when an object is placed 60 cm from the mirror. Which statement best describes the focal length of the mirror?
The focal length of the mirror is - 20 cm
For a concave mirror, the mirror formula is 1/f = 1/v + 1/u, with the sign convention that distances measured against the incident light (i.e. in front of the mirror) are negative.
The object is 60 cm in front of the mirror, so u = −60 cm; the real image is formed 30 cm in front of the mirror, so v = −30 cm. Substituting, 1/f = 1/(−30) + 1/(−60) = −2/60 − 1/60 = −3/60 = −1/20, so f = −20 cm. The negative sign shows the focus is in front of the mirror, as expected for a concave mirror. The other values (+15, −30, +10) do not satisfy the mirror equation.
Hence, the answer is: The focal length of the mirror is − 20 cm.
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