Question

To become familiar with using the image of one instrument as the object of the next and tracing rays through a system of multiple instruments.

Multiple optics refers to any system of more than one optical instrument through which light passes. Most devices related to optics, such as cameras, microscopes, and telescopes, contain multiple optics systems.

In multiple optics, the image of one optical instrument becomes the object of the next one. Thus, in multiple optics problems, you need to find the image created by the first optical instrument that the rays encounter. Then, you will use that image as the object of the next optical instrument, repeating this pattern until you have followed the rays all the way through the system. It is very important to be alert to the geometry and to signs when you find the object distance for one instrument from the location of the previous instrument's image. Sometimes, the image is formed on the virtual side of the instrument, leading to a virtual object. This may sound strange, but in practice, its effect on your calculations is simply to make the object distance negative instead of positive.

Several optical instruments are placed along the x axis, with their axes aligned along the x axis. A plane mirror is located at x=0. A converging lens with focal length 5.00 m is located at x=12.5m. An object is placed at x=22.5m.

Part A: First, find the location of the image created by the lens by itself (as if no other instruments were present).

ANSWER

x =

2.50

m

Part B: Next, find the location of the image created by the plane mirror (after the light has passed through the lens).

ANSWER

x =

-2.50

m

Part C: What is the location of the final image, as seen by an observer looking toward the mirror, through the lens? Keep in mind that the light must pass back through the lens, and thus you must do one more calculation with the thin lens equation.

ANSWER

x =

20.0

m

Part D: First, find the magnitude mlens1 of the magnification of the image created when light from the object passes through the lens the first time (as if the mirror were not present).

ANSWER

mlens1 =

1

Part E: Next, find the magnitude mmirror of the magnification of the plane mirror.

ANSWER

mmirror =

1

Part F: Now find the magnitude mlens2 of the magnification of the image created when light from the object passes through the lens the second time (after reflecting off the mirror).

Part G: What is the magnitude of the magnification of the final image?

Answer 1

Part A : Find the location of the image created by the lens itself.

Using a len's formula, we have

1 / d_0,1 + 1 / d_i,1 = 1 / f

where, d_0,1 = object distance = x₀ - L = [(22.5 m) - (12.5 m)]

f = focal length of converging lens = 5 m

then, we get

1 / d_i,1 = 1 / (5 m) - 1 / (10 m)

1 / d_i,1 = (1 / 10) m

d_i,1 = 10 m

We know that, x₁ = L - d_i,1

x₁ = [(12.5 m) - (10 m)]

x₁ = 2.5 m

Part B : Find the location of the image created by the plane mirror.

Using a mirror formula, we have

1 / d_0,2 + 1 / d_i,2 = 1 / f

where, d_0,2 = object distance = L - d_i,1 = [(12.5 m) - (10 m)]

f = focal length of converging lens =

then, we get

1 / d_i,2 = 1 / () - 1 / (2.5 m)

1 / d_i,2 = - (1 / 2.5) m

d_i,2 = - 2.5 m

We know that, x₂ = d_i,2

x₂ = - 2.5 m

Part C : What is the location of the final image, as seen by an observer looking toward the mirror through the lens?

Using a lens formula, we have

1 / d_0,3 + 1 / d_i,3 = 1 / f

where, d_0,3 = object distance = L - d_i,2 = [(12.5 m) - (-2.5 m)]

f = focal length of converging lens = 5 m

then, we get

1 / d_i,3 = 1 / (5 m) - 1 / (15 m)

1 / d_i,3 = (15 / 2) m

d_i,3 = 7.5 m

We know that, x₃ = L + d_i,3

x₃ = [(12.5 m) + (7.5 m)]

x₃ = 20 m

Part D : Find the magnitude of the magnification of image created when light from an object passes through the lens first time.

m_lens,1 = (d_i,1 / d_0,1)

m_lens,1 = [(10 m) / (10 m)]

m_lens,1 = 1

Part E : Find the magnitude of the magnification of a plane mirror.

m_mirror = - (d_i,2 / d_0,2)

m_mirror = - [(-2.5 m) / (2.5 m)]

m_mirror = 1

Part F : Find the magnitude of the magnification of image created when light from object passes through the lens second time.

m_lens,2 = (d_0,3 / d_i,3)

m_lens,2 = [(7.5 m) / (15 m)]

m_lens,2 = 0.5

Part G : What is the magnitude of the magnification of final image?

M = (m_lens,1) x (m_mirror) x (m_lens,2)

M = (1) x (1) x (0.5)

M = 0.5