An object is placed 5 cm in front of a concave lens of focal length 7 cm. Find the image location by drawing a ray tracing diagram to scale.
To find the image location using a ray tracing diagram, follow these steps:
1. Draw a horizontal line, representing the principal axis of the lens.
2. Draw a vertical line perpendicular to the principal axis at the center of the lens, representing the optical center.
3. Place the concave lens on the principal axis, making sure the vertical line passes through the center of the lens.
4. Mark the distance of 5 cm in front of the lens on the principal axis. This is the location of the object.
5. Draw a ray from the top of the object parallel to the principal axis. This ray will refract through the lens and pass through the focal point on the opposite side of the lens.
6. Draw a ray from the top of the object passing through the optical center of the lens. This ray will continue in a straight line without bending.
7. Where the two refracted rays intersect is the location of the image. Mark this point on the principal axis.
Now, let's determine the image location.
Given:
- Object distance (u) = -5 cm (negative sign indicates that the object is located in front of the lens)
- Focal length (f) = 7 cm
Using the lens formula:
1/f = 1/v - 1/u
Substituting the given values:
1/7 = 1/v - 1/-5
Simplifying the equation:
1/v = 1/7 + 1/5
Now, find the common denominator:
1/v = (5 + 7) / (7 * 5)
1/v = 12 / 35
Taking the reciprocal:
v = 35 / 12 cm
Therefore, the image is located approximately 2.92 cm behind the lens. Mark this point on the principal axis, and that is the location of the image.