A diverging lens located in the y-z plane at x = 0 forms an image of an arrow at x = x₂ = -22.7 cm. The image of the tip of the arrow is located at y = y₂ = 3.8 cm. The magnitude of the focal length of the diverging lens is 46.3 cm.

What is y₁, the y-coordinate of the tip of the object arrow?

A converging lens of focal length f_converging = 15.44 cm is now inserted at x = x₃ = -23.16 cm. In the absence of the diverging lens, at what x co-ordinate, x₄, would the image of the arrow form?

To determine the image of the arrow from the combined converging + diverging lens system, we take the image from the converging lens (in the absence of the diverging lens) to be the object for the diverging lens. If this image is downstream of the diverging lens, the object for the diverging lens is virtual.
All this means is that the rays entering the diverging lens are converging towards a location downstream of the diverging lens. The final image can be calculated using this virtual object distance and the focal length of the diverging lens.

If this description seems unclear to you, you can check out the more detailed description of multiple lens systems given in the Optical Instruments unit.

What is x₅, the x co-ordinate of the final image of the combined system?

$air Soap bubble air A soap film is 127 nm thick. The film is in air and it is illuminated by white light at normal incidence as shown in the figure below. (In the figure the rays have been drawn at an angle to show the multiple reflections and transmissions in the film.) The index of refraction of the soap film is the same as the index of refraction of water n = 1.33. The film is viewed from above and below by a video system which is sensitive to wavelengths from 200 to 1100 nm. 1) When viewed from above in reflection, what is the longest visible wavelength that will appear enhanced? nm Submit 2) When viewed above in reflection, what is the longest visible wavelength that will have the least intensity? nm Submit 3) When viewed from below in transmission, what is the longest visible wavelength that will appear enhanced? nm Submit$
Transcribed Image Text:air Soap bubble air A soap film is 127 nm thick. The film is in air and it is illuminated by white light at normal incidence as shown in the figure below. (In the figure the rays have been drawn at an angle to show the multiple reflections and transmissions in the film.) The index of refraction of the soap film is the same as the index of refraction of water n = 1.33. The film is viewed from above and below by a video system which is sensitive to wavelengths from 200 to 1100 nm. 1) When viewed from above in reflection, what is the longest visible wavelength that will appear enhanced? nm Submit 2) When viewed above in reflection, what is the longest visible wavelength that will have the least intensity? nm Submit 3) When viewed from below in transmission, what is the longest visible wavelength that will appear enhanced? nm Submit

Question

A diverging lens located in the y-z plane at x = 0 forms an image of an arrow at x = x₂ = -22.7 cm. The image of the tip of the arrow is located at y = y₂ = 3.8 cm. The magnitude of the focal length of the diverging lens is 46.3 cm.

What is y₁, the y-coordinate of the tip of the object arrow?

A converging lens of focal length f_converging = 15.44 cm is now inserted at x = x₃ = -23.16 cm. In the absence of the diverging lens, at what x co-ordinate, x₄, would the image of the arrow form?

To determine the image of the arrow from the combined converging + diverging lens system, we take the image from the converging lens (in the absence of the diverging lens) to be the object for the diverging lens. If this image is downstream of the diverging lens, the object for the diverging lens is virtual.

All this means is that the rays entering the diverging lens are converging towards a location downstream of the diverging lens. The final image can be calculated using this virtual object distance and the focal length of the diverging lens.

If this description seems unclear to you, you can check out the more detailed description of multiple lens systems given in the Optical Instruments unit.

What is x₅, the x co-ordinate of the final image of the combined system?

air
Soap bubble
air
A soap film is 127 nm thick. The film is in air and it is illuminated by white light at normal incidence as shown in the
figure below. (In the figure the rays have been drawn at an angle to show the multiple reflections and transmissions in
the film.) The index of refraction of the soap film is the same as the index of refraction of water n = 1.33. The film is
viewed from above and below by a video system which is sensitive to wavelengths from 200 to 1100 nm.
1) When viewed from above in reflection, what is the longest visible wavelength that will appear enhanced?
nm
Submit
2) When viewed above in reflection, what is the longest visible wavelength that will have the least intensity?
nm
Submit
3) When viewed from below in transmission, what is the longest visible wavelength that will appear enhanced?
nm
Submit

Accepted Answer

1). The condition for constructive interference for normal incidence under reflected light in this…