An object is placed 11.3 cm to the left of a diverging lens of focal length -6.51 cm. A converging lens of focal length 11.6 cm is placed a distance of d to the right of the diverging lens. Find the distance d that places the final image at infinity.
To find the distance d that places the final image at infinity, we can use the lens formula and the concept of lens combinations.
The lens formula is given by:
1/f = 1/v - 1/u
Where:
- f is the focal length of the lens,
- v is the image distance,
- u is the object distance.
For the diverging lens, the focal length f1 is given as -6.51 cm and the object distance u1 is given as -11.3 cm (since the object is placed to the left of the lens).
Using the lens formula for the diverging lens, we can calculate the image distance v1:
1/f1 = 1/v1 - 1/u1
Now, for the converging lens, the focal length f2 is given as 11.6 cm. The object distance u2 is given as d (the distance between the lenses).
Since the final image is at infinity, the image distance v2 is also at infinity.
Using the lens formula for the converging lens, we get:
1/f2 = 1/v2 - 1/u2
1/11.6 = 0 - 1/d (because v2 = infinity)
Simplifying the equation, we have:
1/11.6 = -1/d
Cross-multiplying, we get:
d = -11.6
Therefore, the distance d that places the final image at infinity is -11.6 cm.