An object is placed 8 cm in front of a convex lens of focal length 6 cm. Find the image location by drawing a ray tracing diagram to scale. Verify your answer using the lens equation
To find the image location using ray tracing, follow these steps:
1. Draw a horizontal line representing the principal axis of the lens.
2. Place an arrow pointing upward on the left side of the line to represent the object. Label it "O."
3. Draw a line from the top of the object that is parallel to the principal axis until it intersects with the lens. Label this point "A."
4. Draw a line from the top of the object through the center of the lens. Label this point "B."
5. Draw a line through point B and extending to the right side of the principal axis. This is the incident ray.
6. Draw a line from point A to the right side of the principal axis, curving away from the lens. This represents the refracted ray.
7. Draw a line from the right side of the lens, passing through point B, and extending until it intersects with the principal axis. Label this point "I." This is the image location.
Now, to verify the answer using the lens equation, follow these steps:
The lens equation is given by:
1/f = 1/do + 1/di
Where:
- f is the focal length of the lens
- do is the object distance
- di is the image distance
Given:
- f = 6 cm
- do = -8 cm (since the object is placed in front of the lens and its distance is negative)
Substituting the values, we have:
1/6 = 1/-8 + 1/di
Simplifying, we get:
1/6 = -1/8 + 1/di
Multiply both sides by 48 (the common denominator):
8 = -6 + 48/di
Simplifying further:
14 = 48/di
Dividing both sides by 14:
1/di = 14/48
Taking the reciprocal of both sides:
di = 48/14
Simplifying, we get:
di = 24/7 cm
So, the image location is 24/7 cm.
By drawing the ray tracing diagram and using the lens equation, we verify that the image location is 24/7 cm.