An object is placed 6 cm in front of a concave lens of focal length 3 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 of an object placed in front of a concave lens, we can use ray tracing and the lens equation. Here's how you can solve it:

Step 1: Draw a ray tracing diagram:
- Draw the concave lens as a symmetrical shape with a thicker center and thinner edges.
- Locate the optical center (O) of the lens in the middle.
- Mark the principal axis (the horizontal line passing through O).
- Place the object on the principal axis, 6 cm in front of the lens. Label it as "O".
- Draw two incident rays from the top and bottom of the object:
- The first ray should be parallel to the principal axis and refract through the lens, passing through the focal point on the opposite side. Label this ray as "F".
- The second ray should pass through the optical center without changing direction.
- Finally, draw the line where these two refracted rays intersect after passing through the lens. This intersection point is the location of the image. Label it as "I".

Step 2: Measure the distances:
- Measure the distance from the object (O) to the lens. In this case, it is 6 cm.
- Measure the focal length of the lens (f). In this case, it is 3 cm.

Step 3: Apply the lens equation:
The lens equation is given by: 1/f = 1/dₒ + 1/dᵢ, where f is the focal length, dₒ is the object distance, and dᵢ is the image distance.

Since the object is placed in front of the lens, the object distance is negative (-6 cm). We need to solve for the image distance (dᵢ).

Plug in the given values into the lens equation:
1/3 = 1/-6 + 1/dᵢ

Simplifying the equation gives:
1/3 = -1/6 + 1/dᵢ

To combine the fractions, find a common denominator of 6:
2/6 = -1/6 + 1/dᵢ

Since the denominators are the same, we can combine the fractions:
1/6 = 1/dᵢ

Cross-multiplying gives:
dᵢ = 6 cm

So the image is formed 6 cm behind the lens, on the same side as the object.

Step 4: Verify your answer:
To verify the answer, compare the result of the lens equation with the ray tracing diagram. The ray tracing diagram should show that the intersection point labeled "I" is 6 cm behind the lens.

By following these steps, you can find the image location of an object placed in front of a concave lens and verify the answer using the lens equation.