Converging lens has focal lenght 8 cm , at what distance you will have to place the object in the following devices;
1) Collimator of Spectrum
2) Terrestrial Telescope
To find the distance at which you will have to place the object for each of these devices, you need to use the lens formula:
1) Collimator of Spectrum:
The collimator of a spectrum consists of a converging lens. The object distance (u) in this case will be equal to the focal length (f) of the lens.
Plugging these values into the lens formula:
1/f = 1/v - 1/u
Since the object distance (u) is equal to the focal length (f), the lens formula becomes:
1/f = 1/v - 1/f
Rearranging the equation, we find:
1/v = 2/f
Substituting the given focal length (f) as 8 cm:
1/v = 2/8
Simplifying further:
1/v = 1/4
Now, solve for v (the image distance) by taking the reciprocal of both sides:
v = 4 cm
Therefore, the object needs to be placed at a distance of 4 cm from the collimator lens.
2) Terrestrial Telescope:
A terrestrial telescope also uses a converging lens. The object distance (u) in this case will be greater than 2 times the focal length (f).
For a terrestrial telescope, the lens formula is applicable, but the object distance will be greater than 2f.
So, we can assume the object distance (u) to be approximately equal to infinite (∞). Rearranging the lens formula, we get:
1/f = 1/v - 1/u
Since the object distance (u) is very far away, we can consider 1/u as approximately zero. Thus, the lens formula becomes:
1/f ≈ 1/v
Rearranging the equation, we find:
v ≈ f
Substituting the given focal length (f) as 8 cm:
v ≈ 8 cm
Therefore, for a terrestrial telescope, the object needs to be placed at a distance approximately equal to the focal length, which is 8 cm.