Question

(Application) You are asked to design a multiple lens system for the scenarios below. The lenses youhave available to you are:1. converging (f =7.5 cm)2. converging (f =15.0 cm)3. diverging (f = -15.0 cm)Think about the following scenarios:A) Lens 1 makes a real image i1, of which lens 2 makes a real image i2.B) Lens 1 makes a real image i1, of which diverging lens 2 makes a virtual image i2.C) Converging lens 1 makes a virtual image i1, of which converging lens 2 makes a virtual image i2.D) Converging lens 1 makes a virtual image i1, of which lens 2 makes a real image i2.For each scenario, decide:1) What type of lens is lens 1? Lens 2? Why? 2) Where should the object be placed with respect to the focal point to make the indicated type of image?3) Make a schematic drawing for Scenario D only. If you want extra practice, try to makeschematic drawings of the other three scenarios.

Answer 1

Answer:

1) A) Lens converging, B) lens 1 converging

2) A and B object is at a greater distance than its focal

3)

Explanation:

For this exercise we will give some more important characteristics of the lenses.

we use the equation of the constructor

         1 / f = 1 / p + 1 / q

where f is the focal length and p and qlas the distance to the object and image, respectively.

We must also use how the lenses are combined

       1 / = 1 / f₁ + 1 / f₂

where feq is the equivalent focal length and it is assumed that the two lenses are in contact.

By applying the equation of the constructor you get some characteristics of the image

Converging lens

* Object farther than focal length real and inverted image

* Oject after focal virtual image and right

Diverging lens

* for all virtual image distance and right

with this information let's analyze the different configurations

1) let's do an analysis for each scenario

A) since lens 1 and lens 2 create real image they must be converging lenses

B) Lens 1 must be convergent and lens 2 can be of both types

C) Lens 1 can be convergent with the object that is at a shorter distance than at focal point (p <f₁). The same analysis diverges for lens 2, the object that is the image of the other lens is shorter than its focal distance p₂ <f₂

D) the object is at a shorter distance than the focal length p₁ <f₁, the object for this lens is at a greater distance than its focal point p₂> f₂

2) let's analyze for each scenario

A) for each lens the object is at a greater distance than its focal length p₁> f₁ and p₂> f₂

B) for lens 1 p₁> f₁

for lens 2

if it is convergent p₂ <f₂

and if it is divergent any distance is possible

C) lens 1 p₁ <f₁ and for lens 2 p₂ <f₂

D) lens 1 p₁ <f₁ and for lens 2 p₂> f₂

3) see attached

The distance with subscript 1 is measured with respect to line1 and the distance with subscript 2 is measured with respect to the lens with subscript 2