two converging lenses placed L1=20 cm apart. the focal lengths are f1=10 cm and f2=20cm

1) where is the final image located for an object that L2=30cm infront of the first lens?

2)what is the total magnification of the lens system?

*diagram*

{Object}|--l2--|{lens1 = f1}|--L1--|{lens 2=f2}

To find the location of the final image formed by the lens system and the total magnification, we can use the lens formula and the magnification formula.

1) To find the location of the final image, we need to find the effective focal length (feff) of the lens system. The formula to calculate the effective focal length is given by:

1/feff = 1/f1 + 1/f2 - (d/f1 * d/f2)

Where f1 and f2 are the focal lengths of the individual lenses, and d is the distance between the lenses.

Given:
f1 = 10 cm
f2 = 20 cm
d = L1 = 20 cm

1/feff = 1/10 + 1/20 - (20/10 * 20/20)
1/feff = 1/10 + 1/20 - 1/10
1/feff = 1/20

Therefore, the effective focal length (feff) for the lens system is 20 cm. Now, we can use this value to find the location of the final image.

To calculate the image position, we can use the lens formula:

1/f1 = 1/v1 - 1/u1
1/f2 = 1/v2 - 1/u2

Where:
v1 and v2 are the distances of the final image from lens 1 and lens 2, respectively.
u1 and u2 are the distances of the object from lens 1 and lens 2, respectively.

Given:
u1 = L2 = 30 cm
u2 = L1 - u1 = 20 cm (since L1 is the distance between the lenses)

Using the lens formula for lens 1, we have:
1/10 = 1/v1 - 1/30
1/v1 = 1/10 + 1/30
1/v1 = 4/30
v1 = 30/4
v1 = 7.5 cm

Using the lens formula for lens 2, we have:
1/20 = 1/v2 - 1/20
1/v2 = 1/20 + 1/20
1/v2 = 2/20
v2 = 20/2
v2 = 10 cm

Since the final image is formed by lens 2, the final image location will be v2, which is 10 cm.

Therefore, the final image is located 10 cm in front of the second lens.

2) To find the total magnification of the lens system, we can use the magnification formula for each lens:

m1 = -v1/u1
m2 = -v2/u2

Where m1 and m2 are the magnifications produced by lens 1 and lens 2, respectively.

Using the values we calculated:
m1 = -7.5 cm / 30 cm
m2 = -10 cm / 20 cm

To find the total magnification (mtotal), we can multiply the individual magnifications (m1 and m2):

mtotal = m1 * m2

Substituting the values:
mtotal = (-7.5 cm / 30 cm) * (-10 cm / 20 cm)
mtotal = 0.25

Therefore, the total magnification of the lens system is 0.25.