Optics problems please help?

Question

A camera has a single convex lens of focal length 50mm, it can be moved relative to the film plane such that the lens film distance may be varied between 50mm and 70mm.

The photographer finds it necessary to focus on a object 120mm in front of the lens. In order to produce a sharp image the photographer needs to insert an extension tube of length x between the lens and the camera.

Find the minimum length of this tube?

Investigate the effect of this tube on the furthest object that may be imaged by this camera?

please help!!

The extension tube is removed, the photographer now wants to take some macro photos with high magnification of some insects. He places a covex magnifying lens of focal length 35mm directly in front of the camera lens....

Find the shortest distance that the insect can be placed from the camera lens, and find the angular magnification that is achieved with the insect at this distance over what can be achieved without the magnifying lens??

Answer 1

u = object distance,

v = image distance,

f = focal length,

Measurements in cm.

With the tube:

1 / 12 + 1 / v = 1 / 5

v = 8.57 cm.

Minimum tube length

= 8.57 - 7 = 1.57 cm.

Furthest object which can be focused without tube:

1 / u + 1 / 5 = 1 / 5

u is infinite.

Furthest object which can be focused with tube:

1 / u + 1 / (5 + 1.57) = 1 / 5

u = 20.9 cm.

Shortest distance for insect with additional lens:

1 / u + 1 / 7 = 1 / 3.5 + 1 / 5

u = 2.92 cm.

Magnification with additional lens:

7 / 2.92 = 2.4.

Magnification without additional lens.

Shortest u:

1 / u + 1 / 7 = 1 / 5

u = 17.5 cm.

Magnification = 7 / 17.5 = 0.4.

Magnification factor with additional lens is 2.4 / 0.4 = 6 times as great as that without.