Need help with later magnification and location

[dkgrubby]

Need help with later magnification and location!

Two lenses, with = +20.0 and = +30.0 , are placed on the axis, as shown in the figure. An object is fixed 50.0 to the left of lens 1, and lens 2 is a variable distance to the right of lens 1.

Part A
Find the lateral location of the final image relative to lens 2 for the case = 100 .
=54.5
Correct


Part B
Find the lateral magnification of the final image relative to lens 2 for the case = 100 .
=

One attempt remaining; Try Again


Part C
Find the lateral location of the final image relative to lens 2 for the case = 30.0 .
=3.00
Correct


Part D
Find the lateral magnification of the final image relative to lens 2 for the case = 30.0 .
=

Try Again; 4 attempts remaining


Part E
Find the lateral location of the final image relative to lens 2 for the case = 0.
=


Try Again; 5 attempts remaining


Part F
Find the lateral magnification of the final image relative to lens 2 for the case = 0.
=



Part G
Show that your result for part E agrees with the relation for the effective focal length of two lenses in contact, .
Essay answers are limited to about 500 words (3800 characters maximum, including spaces).

 

[jbsteele]

When two lenses of focal lengths f1 and f2 are in contact, the effective focal length is given by the equation: f = (f1f2)/(f1+f2). In this case, f1=20 m and f2=30 m, so the effective focal length is f = (20*30)/(20+30) = 12 m. The lateral location of the final image relative to lens 2 can be found by applying the thin lens equation 1/p+1/q = 1/f, where p is the object distance, q is the image distance, and f is the focal length. Since the object is 50 m from lens 1 and the focal length is 12 m, q = -12 m. This means that the lateral location of the final image relative to lens 2 is 3 m, which agrees with the result obtained in Part E. Therefore, this shows that the result for part E agrees with the relation for the effective focal length of two lenses in contact.