A diverging lens has a focal length of -22 cm. Find the image distance when an object is placed 41 cm from the lens.
To find the image distance in this scenario, we can use the lens formula:
1/f = 1/v - 1/u
Where:
- f represents the focal length of the lens,
- v is the image distance from the lens, and
- u is the object distance from the lens.
Given that the focal length of the diverging lens is -22 cm and the object distance is 41 cm, we can substitute these values into the lens formula:
1/-22 = 1/v - 1/41
Now, we need to solve the equation to find the value of v. Let's go step by step:
Multiply every term by -22 * 41 to eliminate the fractions:
[(-22) * 41] * (1/-22) = [(-22) * 41] * (1/v - 1/41)
-41 = -22 * 41 / v + (-22) * 41 / 41
Simplify:
-41 = -22 * 41 / v - 22
Rearrange:
-41 + 22 = -22 * 41 / v
-19 = -902 / v
Cross-multiply:
-19v = -902
Divide by -19:
v = -902 / -19
v = 47.47 cm (rounded to two decimal places)
Therefore, the image distance is approximately 47.47 cm when the object is placed 41 cm from the lens.