a parallel beam of light which formed upon a converging lens arrange with its axis parallel to the beam is brought to focus a 30cm of the lens the light that passes through the second converging lens of focal length 5 cm is 34 cm from the first length.Determine the position of the final image.
What is the name given to the optical instrument with this arrangement of lenses?
To determine the position of the final image, we can use the lens formula:
1/f = 1/v - 1/u,
where:
- f is the focal length of the lens,
- v is the image distance from the lens, and
- u is the object distance from the lens.
For the first converging lens, the image distance (v1) is given as 30 cm, and the object distance (u1) can be considered as infinity for a parallel beam of light incident on a lens. So we have:
1/f1 = 1/v1 - 1/u1 = 1/30 - 0,
since 1/u1 is zero. Therefore, the focal length of the first converging lens (f1) is 30 cm.
For the second converging lens, the image distance (v2) is given as 34 cm. We need to find the object distance (u2) from the second lens to determine the position of the final image.
Now, using the lens formula for the second lens, we have:
1/f2 = 1/v2 - 1/u2,
where f2 is the focal length of the second lens.
The focal length (f2) is given as 5 cm, and the image distance (v2) is given as 34 cm. Solving for u2, we have:
1/5 = 1/34 - 1/u2,
1/u2 = 1/34 - 1/5,
1/u2 = (5 - 34)/(5 * 34),
1/u2 = -29/170,
u2 = -170/29 cm.
Since the object distance (u2) is negative, it means that the object is placed on the same side as the incoming light.
Hence, the position of the final image is 170/29 cm from the second converging lens.
The optical instrument with this arrangement of lenses is called a compound microscope.