Telephoto lens. Use the formula from Exercise 67 to find the image distance i for an object that is 2,000,000 mm from a 250-mm telephoto lens. (Section 6.7 (1/f = 1/0 +1/i)
1/i = 1/250 - 1/ (2*10^9)
i=25.
To find the image distance i for an object that is 2,000,000 mm from a 250-mm telephoto lens using the formula (1/f = 1/o + 1/i), follow these steps:
1. Identify the given values:
- Object distance (o) = 2,000,000 mm
- Focal length (f) = 250 mm
2. Substitute the given values into the formula:
(1/f) = (1/o) + (1/i)
Substitute the values:
(1/250) = (1/2,000,000) + (1/i)
3. Simplify the equation:
To add fractions, you need a common denominator. The common denominator in this case is 2,000,000 * 250 = 500,000,000.
Multiply both sides of the equation by the common denominator:
(500,000,000 / 250) = (500,000,000 / 2,000,000) + (500,000,000 / i)
Simplify both sides:
2,000,000 = 250 + (500,000,000 / i)
4. Solve for i:
Subtract 250 from both sides of the equation:
2,000,000 - 250 = 500,000,000 / i
Simplify the left side:
1,999,750 = 500,000,000 / i
Multiply both sides by i to get i out of the denominator:
(1,999,750) * i = 500,000,000
Divide both sides by (1,999,750) to isolate i:
i = 500,000,000 / 1,999,750
Calculate the value:
i ≈ 250.125 mm
Therefore, the image distance (i) for an object that is 2,000,000 mm from a 250-mm telephoto lens is approximately 250.125 mm.