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. Verify your answer using the lens equation.

I am confused on what numbers would be negative in my formula of 1/f=1/v+1/u.

When using the lens equation, it's important to assign proper signs to the distances involved. The convention used is as follows:

- Distances measured in the direction from the object towards the lens are taken as positive.
- Distances measured in the direction opposite to the object are taken as negative.

Here's how you can determine the signs for the variables in the lens equation when dealing with a concave lens:

1. Object distance (u): The object is placed 5 cm in front of the lens, so it is to the left of the lens. Since distances to the left are traditionally taken as negative, the object distance (u) will be -5 cm.

2. Image distance (v): To find the image location, you will need to draw a ray tracing diagram, as mentioned in the question. By doing so, you can determine the image distance (v) and verify the answer later.

Now let's use the lens equation to assist with determining the image distance (v):

1/f = 1/v + 1/u

Since the focal length (f) is given as 7 cm, and the object distance (u) is -5 cm, we can plug these values into the equation:

1/7 = 1/v + 1/(-5)

Simplifying:

1/7 = 1/v - 1/5

To combine the fractions, we find the common denominator, which is 35:

5/35 = 35/v - 7/35

Now, combine the fractions:

5/35 = (35 - 7v) / 35

Cross-multiplying:

5(35 - 7v) = 35

175 - 35v = 35

Collecting like terms:

-35v = 35 - 175

-35v = -140

Dividing both sides by -35:

v = -140 / -35

v = 4 cm

By using the lens equation, we find that the image distance (v) is 4 cm. Hence, the negative sign indicates that the image is formed on the same side as the object, meaning it is a virtual image.

To verify this result, you can also draw a ray tracing diagram (to scale) and observe where the converging rays intersect.