Two converging lenses with focal lengths 5 cm and 30 cm are placed 35 cm apart. Rays from a very distant object are impinged on the lens system parallel to the principal axis. What is the refractive power of the combination of these two lenses?
What you have is a confocal telescope. The focal point of both lenses is a common point between them. For such an optical system, the magnification is the ratio of the focal lengths, or in this case 6. Not very powerful.
It is not called "refractive power" in any optics textbook I have ever seen, but fashions change.
To find the refractive power of the combination of these two lenses, we need to use the lens maker's formula. The lens maker's formula relates the focal length (f) of a lens to its refractive index (n) and the radii of curvature of its surfaces (R1 and R2).
The formula is given by:
1/f = (n - 1) * (1/R1 - 1/R2)
Since we have two lenses in this case, we need to calculate the effective focal length (feff) of the combination.
The lens formula for two lenses in contact is:
1/feff = 1/f1 + 1/f2 - d/(f1 * f2)
Where f1 and f2 are the individual focal lengths of the lenses, and d is the distance between the lenses.
Given:
f1 = 5 cm
f2 = 30 cm
d = 35 cm
Let's first calculate 1/feff using the lens formula:
1/feff = 1/f1 + 1/f2 - d/(f1 * f2)
Substituting the given values:
1/feff = 1/5 + 1/30 - 35/(5 * 30)
Simplifying the expression on the right side:
1/feff = 6/30 + 1/30 - 35/150
1/feff = (6 + 1 - 35)/150
1/feff = -28/150
Now, we can use the lens maker's formula to find the refractive power (P) of the combination:
1/feff = (n - 1) * (1/R1 - 1/R2)
Since we have parallel rays from a distant object, the object is at infinity. Hence, the rays are practically parallel to each other. Therefore, we can assume that the object is at infinity for our calculations.
For an object at infinity, the rays are parallel to the principal axis, and the lens formula reduces to:
P = 1/f
Substituting -28/150 for 1/feff, we get:
P = -150/28
Simplifying the fraction gives us:
P ≈ -5.36
Therefore, the refractive power of the combination of these two lenses is approximately -5.36 Diopters.