Calculating Angular Magnification and Image Position in Compound Lens Systems

[Darth Frodo]

Homework Statement

1. An object is placed 1.5m in front of a convex lens of focal length 500mm. Find the position of the image formed and state its nature.

2. A second convex lens of focal length 25mm is placed 770mm behind the first convex lens. Find the position of the final image formed and state whether the image is real or virtual.

3. Find the angular magnification for the final image if it is formed at infinity.

The Attempt at a Solution

1.$\frac{1}{u} + \frac{1}{v} = \frac{1}{f}$
$\frac{1}{1500} + \frac{1}{v} = \frac{1}{500}$
$v = 750mm$

$m = \frac{-v}{u} = \frac{-750}{1500} = -0.5$

Image is Real as v > 0
Image is Diminished as |m|<1
Image is Inverted as m < 0

2. $\frac{1}{u} + \frac{1}{v} = \frac{1}{f}$
$\frac{1}{20} + \frac{1}{v} = \frac{1}{25}$
$v = -100$

Image is virtual as v < 0

3. This is the part I don't know how to do. Any advice would be appreciated.

 

[Sunil Simha]

You can define angular magnification as
$M_A=\frac{tanθ_1}{tanθ_2}$

Where θ₁ is the angle subtended by the first image at the first lens and θ₂ is the angle subtended by the second image at the second lens.(Check out the attachment)

Under what condition is the final image at infinity?