Final answer:
The position of the image formed by the concave mirror when an object is placed 50 cm in front of it and the radius of curvature is 60 cm, is 30 cm in front of the mirror, indicating a real image.
Step-by-step explanation:
To calculate the position of the image formed by a concave mirror, we can use the mirror equation: \( \frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i} \), where f is the focal length, d_o is the object distance, and d_i is the image distance.
The radius of curvature R is related to the focal length by f = \frac{R}{2}. Therefore, for a concave mirror with a radius of curvature of 60 cm, the focal length is 60 cm / 2 = 30 cm. With the object placed 50 cm in front of the mirror, d_o = -50 cm (the negative sign indicates that the object is in front of the mirror).
Using the mirror equation, we have: \( \frac{1}{-30 cm} = \frac{1}{-50 cm} + \frac{1}{d_i} \), which simplifies to \( \frac{1}{d_i} = \frac{1}{-30 cm} - \frac{1}{-50 cm} \).
Solving for d_i, we find that d_i = -30 cm. The negative sign indicates the image is formed on the same side as the object, which implies it is a real image. Hence, the correct position of the image formed is 30 cm in front of the mirror.
Therefore, the correct answer is:
a) 30 cm