Final answer:
The image location and magnification for a small bulb placed 50 cm from a convex lens with a concave mirror following it can be found by using the lens equation for the lens and mirror equation for the concave mirror, and calculating the respective magnifications.
Step-by-step explanation:
Finding the Image Location and Magnification
To find the location and magnification of a small bulb sitting 50 cm from a thin convex lens followed by a concave mirror, we apply the algebraic method using the lens and mirror equations.
First, we determine the image formed by the convex lens using the thin-lens equation:
1/f = 1/do + 1/di
Where:
f is the focal length of the lens (15 cm),
do is the object distance from the lens (50 cm),
di is the image distance from the lens (to be determined).
Plugging in the values, we calculate the image distance di for the lens.
Once we have the image distance for the lens, we use the mirror equation to find the image formed by the concave mirror:
1/f' = 1/do' + 1/di'
Where:
F is the focal length of the mirror (half the radius of curvature, so 5 cm),
do' is the object distance from the mirror (30 cm plus the lens image distance),
di' is the image distance from the mirror (to be determined).
The final magnification is the product of the magnification of the lens and the magnification of the mirror, calculated using the magnification equations:
m_lens = -di/do and m_mirror = -di'/do'
By solving these equations step-by-step, we would find the location and magnification of the bulb's image as formed by the system of the convex lens and concave mirror.