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.
To find the image location using ray tracing, you can follow these steps:
Step 1: Draw a straight line to represent the principal axis.
Step 2: Mark the location of the concave lens on the principal axis. The focal length (f) of the lens is 7 cm, so mark a point 7 cm from the lens.
Step 3: Place the object on the principal axis, 5 cm in front of the lens (towards the left).
Step 4: Draw a ray from the top of the object parallel to the principal axis. This ray will pass through the focal point on the opposite side of the lens after refraction.
Step 5: Draw a ray from the top of the object that passes through the center of the lens (the optical center). This ray will not change direction after passing through the lens.
Step 6: Lastly, draw a ray from the top of the object that passes through the focal point on the same side of the lens. After refraction, this ray will become parallel to the principal axis.
Step 7: Continue the extended rays on the opposite side and locate where they intersect. This point of intersection represents the image location.
To verify the answer using the lens equation, we can use the formula:
1/f = 1/v - 1/u
Where:
f = focal length of the lens (7 cm)
v = image distance
u = object distance
Given that the object distance (u) is 5 cm:
1/7 = 1/v - 1/5
To simplify the equation, we can find the common denominator:
(5v - 7v) / (7 * v * 5) = (5 - 7) / (5 * 7)
-2v / (7 * v * 5) = -2 / 35
Canceling out the common factors, we are left with:
-2 / (7 * 5) = -2 / 35
Therefore, the image distance (v) is also equal to 35 cm.
By applying the lens equation, we have verified that the image distance is 35 cm which matches the result obtained through ray tracing.