AP Physics 2 Exam Question:

A convex lens with a focal length of 15 cm is placed in front of an object that is located 10 cm from the lens. A virtual, upright, and magnified image is formed on the other side of the lens.

a) Calculate the position of the image. b) Determine the magnification of the lens. c) Describe the characteristics of the image formed by the lens.

Answer:

a) To calculate the position of the image, we can use the lens equation formula:

1/f = 1/o + 1/i

Where:

• f is the focal length of the lens
• o is the object distance from the lens (positive for objects on the same side as the incident light)
• i is the image distance from the lens (positive for virtual images)

Given: f = 15 cm o = 10 cm

By substituting the values into the equation, we can solve for i:

1/15 = 1/10 + 1/i

Multiplying through by the common denominator (10i), we get:

10i = 15i + 15(10)

Simplifying the equation, we find:

5i = 15(10)

5i = 150

Dividing both sides by 5, we find:

i = 30 cm

Therefore, the image is formed 30 cm from the convex lens.

b) The magnification of the lens can be calculated using the magnification formula:

magnification (m) = -i/o

Given: o = 10 cm i = 30 cm

Substituting the values into the formula, we get:

magnification (m) = -30/10

Simplifying the equation, we find:

magnification (m) = -3

Therefore, the magnification of the lens is -3, indicating that the image formed is three times larger than the object and is inverted.

c) Based on the information given, we can determine the characteristics of the image formed by the lens:

• The image formed is virtual since the image distance (30 cm) is positive.
• The image formed is upright since the magnification (-3) is negative.
• The image formed is magnified since the magnification (-3) is greater than 1.
• The image formed is located on the opposite side of the lens as the object, indicating that it is a virtual image.

Thus, the characteristics of the image formed by the lens are virtual, upright, and magnified.