Final answer:
Correct option: (a) Real, -2
The nature of the image formed by a concave mirror placed 30 cm away from an object with a focal length of 20 cm is real and the magnification is -2.
Step-by-step explanation:
The nature and magnification of the image formed by a concave mirror can be determined using the mirror formula:
1/f = 1/do + 1/di
In this case, the object distance (do) is 30 cm and the focal length (f) is 20 cm.
Substituting these values, we have:
1/20 = 1/30 + 1/di
Simplifying the equation, we find the image distance (di) to be -60 cm.
Since the image distance is negative, the image is real and is formed on the opposite side of the lens from the object.
To calculate the magnification, we use the formula:
magnification = di/do
Substituting the values, we get:
magnification = -60/30
= -2
Therefore, the correct answer is (a) Real, -2.