Question

An object is 28 cm in front of a diverging lens with a focal length of -14 cm.

A) Use ray tracing to determine the location of the image.
Express your answer with the appropriate units. Enter positive value if the image is on the other side from the lens and negative value if the image is on the same side.
B) Is the image upright or inverted?
C) Is the image real or virtual?

Answer 1

To determine the location of the image using ray tracing, we need to draw two rays from the object. The image is formed on the same side as the object and is upright, making it a virtual image.

Step-by-step explanation:

A) To determine the location of the image using ray tracing, we need to draw two rays from the object. The first ray is parallel to the principal axis and will refract through the lens as if it had come from the focal point on the same side as the object. The second ray passes through the center of the lens and does not change direction.

When these two rays are extended behind the lens, they appear to intersect at a point. This point is the location of the image. In this case, since the image is on the same side as the object, the image distance will be negative. Therefore, the location of the image is -4 cm.

B) The image is formed on the same side as the object, which means it is upright.

C) Since the image is formed on the same side as the object and is upright, it is a virtual image.

Answer 2

Using ray tracing, we can determine that the image formed by a diverging lens is on the same side as the object, but closer to the lens. The image distance is calculated to be -56 cm.

Step-by-step explanation:

To determine the location of the image formed by a diverging lens, we can use ray tracing. In this case, the object is 28 cm in front of the lens and the focal length of the lens is -14 cm. Since the focal length is negative for a diverging lens, the image formed will always be virtual and on the same side as the object.

Using ray tracing, we can draw two rays. Ray 1 is drawn parallel to the axis and will appear to come from the focal point on the same side as the object. Ray 2 is drawn through the center of the lens and will not change its path. The two rays will appear to diverge from a common point, locating the virtual and upright image. The location of the image can be calculated using the lens formula:

1/f = 1/di - 1/do

where f is the focal length, di is the image distance, and do is the object distance. Plugging in the values, we get:

1/-14 = 1/di - 1/28

Solving for di, we find that the image distance is -56 cm. Since the image distance is negative, the image is on the same side as the object, but closer to the lens.