Final answer:
The power of the convex lens is found using the lens formula, which with the given conditions results in a focal length of -20 cm, converting to power yields -5 diopters, which is answer choice (B).
Step-by-step explanation:
To find the power of a convex lens which forms a real and inverted image of magnification -1 of an object placed at a distance of 20 cm from its optical centre, you can use the lens formula:
\(\frac{1}{f} = \frac{1}{v} - \frac{1}{u}\)
Here, v is the image distance, u is the object distance, and f is the focal length. Since the magnification (m) = -1, it implies that the image distance v is equal to -20 cm (negative because the image is formed on the opposite side of the lens). The object distance u is -20 cm (negative in accordance with the sign convention for lenses).
Substituting the values:
\(\frac{1}{f} = \frac{1}{-20} - \frac{1}{-20} = 0 - \frac{1}{20}\)
\(\frac{1}{f} = -\frac{1}{20}\)
Hence, f = -20 cm. Now, power P is the reciprocal of the focal length in meters. Converting the focal length to meters:
f = -0.20 m
So, P = \(\frac{1}{-0.20}\) = -5 diopters.
Thus, the correct answer is (B) -5 diopters.