Concept explainers
An achromatic lens is made of two very thin lenses, placed in contact, that have focal lengths f1 = -27.8 cm and f2= +25.3 cm. (a) Is the combination converging or diverging? (b) What is the net focal length?
Part (a)To determine:
The net focal length of the combination of the two thin lenses.
Answer to Problem 46P
Solution:
The net focal length of the combination of the two thin lenses in contact is found to be +281 cm.
Explanation of Solution
Given:
The focal length of the thin lenses
Formula used:
The net focal length of the combination of lenses is given by
Calculation:
Use the given values of in the expression to calculate the value of the net focal length.
Part (b)To determine:
If the given combination of lenses is converging or a diverging.
Answer to Problem 46P
Solution:s:
The given combination of the lenses is a converging lens.:
Explanation of Solution
Given:
The focal length of the thin lenses
The focal length of a converging lens is positive and that of a diverging lens is negative. When two thin lenses are kept in contact, the combination may behave as a converging lens if the equivalent focal length of the combination is positive. The combination may behave as a diverging lens if the equivalent focal length is negative.
From the previous section, it can be seen that the equivalent focal length of the combination of the given lenses has a value +281 cm. Since the focal length is positive, the combination functions as a converging lens.
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