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 a ray tracing diagram, we can follow these steps:
Step 1: Draw the Principal Axis
Draw a horizontal line representing the principal axis of the convex lens. This line will pass through the center of the lens.
Step 2: Mark the Lens
Draw a vertical line through the center of the lens to mark its location on the principal axis. Label it as "C" for the center of the lens.
Step 3: Place the Object
Measure 8 cm from the left of the lens and mark a point on the principal axis. Label it as "O" for the object.
Step 4: Draw Incident Ray
Draw a straight line from the top of the object (O) to the top of the lens. This is the incident ray.
Step 5: Pass the Ray through the Focal Point
Draw a dashed line passing through the lens, parallel to the principal axis. This line should bend and pass through the focal point on the right side of the lens. Label this point as "F" for the focal point.
Step 6: Draw the Refracted Ray
At the point where the incident ray intersects the lens, draw a line to the point where the dashed line intersects the lens. This is the refracted ray.
Step 7: Find the Point of Intersection
Extend the refracted ray from step 6 until it intersects with the principal axis. Mark this point as "I" for the image.
Step 8: Measure the Image Distance
Measure the distance between the image point (I) and the lens. This will give you the image distance.
To verify these results using the lens equation, we can use the following formula:
1/f = 1/di - 1/do
where:
- f is the focal length of the lens (6 cm)
- di is the image distance (distance from lens to image)
- do is the object distance (distance from lens to object)
Given that the object distance (do) is -8 cm (since the object is placed in front of the lens) and the focal length (f) is 6 cm, we can substitute these values into the lens equation:
1/6 = 1/di - 1/-8
Simplifying the equation further:
1/6 = 1/di + 1/8
Next, we can find a common denominator and solve for di:
8 + 6 = 48/di
14di = 48
di = 48/14
di ≈ 3.43 cm
So, the image distance is approximately 3.43 cm.
To find the image location using a ray tracing diagram, follow these steps:
Step 1: Draw the lens. Use a ruler to draw a horizontal line to represent the lens. Label it as "Lens."
Step 2: Mark the focal point. From the left side of the lens, measure 6 cm and mark a dot. Label it as "F" to represent the focal point.
Step 3: Mark the object. From the left side of the lens, measure 8 cm and mark a dot. Label it as "O" to represent the object.
Step 4: Draw three rays. Draw three rays from the object, parallel to the principal axis (horizontal line passing through the center of the lens), through the focal point, and through the center of the lens.
Step 5: Ray 1: Parallel ray. Draw a ray from point O parallel to the principal axis. When this ray reaches the lens, it will refract and pass through the focal point F.
Step 6: Ray 2: Focal ray. Draw a ray from point O through the focal point F. This ray will refract and become parallel to the principal axis after passing through the lens.
Step 7: Ray 3: Center ray. Draw a ray from point O through the center of the lens. Since it passes through the center, it will not change its path.
Step 8: Mark the point where the rays intersect. The point where these three rays intersect after refraction will be the location of the image. Label it as "I."
Step 9: Measure the image distance. Measure the distance between the lens and the image point I and record it. Let's call it "di."
Now, let's verify the answer using the lens equation:
The lens equation is:
1/f = 1/di - 1/do
Where f is the focal length of the lens, di is the image distance, and do is the object distance.
Given:
f = 6 cm
do = -8 cm (negative sign indicates that the object is on the same side as the light source)
Plugging in the values, we get:
1/6 = 1/di - 1/-8
Simplifying the equation:
1/6 = 1/di + 1/8
Combining the fractions:
1/6 = (8 + di)/8di
Cross-multiplying:
8di = 6(8 + di)
Expanding:
8di = 48 + 6di
Bringing like terms to one side:
8di - 6di = 48
Simplifying:
2di = 48
Dividing both sides by 2:
di = 24 cm
Therefore, the image distance (di) is 24 cm.
To determine the image location, measure 24 cm to the right of the lens along the principal axis from the point where you drew the lens. Mark this point as "I."
By following these steps, you will find the image location using the ray tracing diagram and verify it using the lens equation.
1/f=1/di + 1/do
1/6=1/di + 1/8
Solve for ‘di’