Question

A concave mirror of radius of curvature 10 cm is placed 30 cm from a thin convex lens of focal length 15 cm. Find the location and magnification of a small bulb sitting 50 cm from the lens by using the algebraic method.

Answer 1

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.

Answer 2

Using the algebraic method, the location of the image can be found using the formula for the location of the image formed by a convex lens. The magnification of the small bulb can be found using the formula for magnification.

Step-by-step explanation:

Using the algebraic method, we can find the location and magnification of the small bulb. Let's start by finding the location of the image. The formula for the location (distance) of the image formed by a convex lens is given by:

{1/f = 1/v - 1/u}

where f is the focal length of the lens, v is the distance of the image from the lens, and u is the distance of the object from the lens. In this case, the focal length of the lens is 15 cm, the distance of the object from the lens is 50 cm, and we need to find the distance of the image from the lens.

Substituting the values into the formula:

{1/15 = 1/v - 1/50}

Solving for v, we get:

v = 30 cm

Therefore, the image is located 30 cm from the lens.

To find the magnification, we can use the formula:

{magnification (m) = -v/u}

where v is the distance of the image from the lens and u is the distance of the object from the lens. Substituting the values into the formula:

{m = -30/50}

Simplifying the expression, we get:

m = -0.6

Therefore, the magnification of the small bulb is -0.6.