A converging lens (f1 = 24.0 cm) is located 56.0 cm to the left of a diverging lens (f2 = -28.0 cm). An object is placed to the left of the converging lens, and the final image produced by the two-lens combination lies 20.3 cm to the left of the diverging lens. How far is the object from the converging lens?
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To find the distance of the object from the converging lens, we can use the lens formula. The lens formula is given by:
1/f = 1/v - 1/u
Where:
f = focal length of the lens
v = image distance
u = object distance
Let's use the given information to solve the problem step by step:
1. Given that the focal length of the converging lens (f1) is 24.0 cm. Therefore, f1 = +24.0 cm (since it's a converging lens).
2. Given that the focal length of the diverging lens (f2) is -28.0 cm. Therefore, f2 = -28.0 cm (since it's a diverging lens).
3. The distance between the converging lens and diverging lens is given as 56.0 cm. Let's say the distance between the object and the converging lens is x cm.
4. The final image distance produced by the two-lens combination lies 20.3 cm to the left of the diverging lens. Therefore, the image distance (v) for the diverging lens is -20.3 cm.
5. Now we can use the lens formula for the converging lens:
1/f1 = 1/v1 - 1/u1
Substituting the values:
1/24 = 1/-20.3 - 1/x
Simplifying the equation:
1/24 = (-1/20.3) - 1/x
6. Rearranging the equation to solve for x:
1/x = 1/24 + 1/20.3
Taking the reciprocal:
x = 1 / (1/24 + 1/20.3)
Calculating the value of x:
x ≈ 13.3 cm
Therefore, the object is approximately 13.3 cm away from the converging lens.