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, we can follow these steps:
Step 1: Draw the lens
Start by drawing a horizontal line to represent the principal axis of the convex lens. Then, draw a vertical line crossing the principal axis to indicate the location of the lens. Label the lens with its focal length, which in this case is 6 cm. Make sure to scale the diagram accurately.
Step 2: Place the object
Measure 8 cm from the left of the lens on the principal axis and mark it as the location of the object. Label it "O" to represent the object.
Step 3: Draw parallel rays
Draw two parallel rays from the top and bottom of the object. Since the object is located on the left side of the lens, the rays will pass through the lens and refract according to the rules of refraction.
Step 4: Ray passing through the center
Draw a ray passing straight through the center of the lens. This ray will continue in a straight line without refracting as it passes through the center of the lens.
Step 5: Ray passing through the focal point
Draw a ray from the top of the object, parallel to the principal axis, that passes through the focal point on the opposite side of the lens. The ray will refract and pass through the focal point on the same side of the lens.
Step 6: Ray tracing
Draw a line connecting the point where the first ray intersects the principal axis (after refraction) with the point where the second ray intersects the principal axis (after refraction). This line represents the path of the refracted rays. The point where this line intersects the principal axis is the location of the image. Label it "I" to represent the image.
Step 7: Measure the image location
Measure the distance from the lens to the image point on the principal axis. This will give you the image distance. In this case, the image distance is, let's say, 12 cm.
Step 8: Verify using the lens equation
The lens equation relates the object distance (o), the image distance (i), and the focal length (f) of a lens:
1/f = 1/o + 1/i
Substituting the given values, we have:
1/6 = 1/8 + 1/i
Simplifying the equation, we find:
1/i = 1/6 - 1/8 = (4 - 3)/24 = 1/24
Taking the reciprocal of both sides, we get:
i = 24 cm
Comparing this with our earlier measurement, we can see that the image location determined by the lens equation (24 cm) matches the image location obtained from the ray tracing diagram (12 cm).
Thus, the image is located 12 cm to the right of the convex lens.