The focal lengths of the converging and diverging distance lenses are +15 and -2
ID: 1551838 • Letter: T
Question
The focal lengths of the converging and diverging distance lenses are +15 and -20 cm respectively. The distance between them is 50 cm and the object is placed 10 cm to the left of the converging lens. a. Determine the location of the first image and magnification. b. Determine the second object distance. c. Determine the final image distance and its magnification. d. Is the final image real or virtual? Find the magnification is the image inverse or upright? Say, you want to measure the difference Delta lambda between two spectrum lines of Na around 589 nm. In order to make the best measurement, you want to measure in the highest possible order m. You have two grating with, 3000 and 4500 grooves /cm, respectively. Find the maximum orders at which the measurement can be done using both gratings and compare (find their ratio) the angular differences, if they are given by delta theta = m delta lambda /d cos theta_m. Which grating will you choose to make a better measurement?Explanation / Answer
A) by lens formula
- 1/u +1/v =1 /f
1/v =1/15 - 1/10
v = 1/ (1/15 - 1/10)
= - 30cm
Image is 30 cm left of left lens
Magnification =30/10= 3
B) second object distance = 30+50 = 80cm
C) again using the same formula,
1/80 + 1/v = - 1/20
v = 1/(-1/20 - 1/80) = - 16cm
16 cm left of right lens
Magnification = 16/80 = 0.2
D)virtual, total magnification =3*0.2=0.6
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