Combination Lenses
Two converging lenses with focal lengths of 40 cm and 20 cm are 10 cm apart. A 2.0-cm-tall object is 15 cm in front of the 40-cm-focal-length lens.
Calculate the image position (relative to the second lens) and its height.
s'_2 = 49 cm, h′ = 4.6 cm
If a diffraction grating produces a third-order bright spot for red light (of wavelength 700 nm) at from the central maximum, at what angle will the second-order bright spot be for violet light (of wavelength 400 nm)?
theta_violet = 20.2 degrees
A converging lens with a focal length of 7.00 cm forms an image of a 4.00-mm-tall real object that is to the left of the lens. The image is 1.30 cm tall and upright. Is the image real or virtual?
The image is virtual.
A 35-mm camera has a standard lens with focal length 50 mm and can focus on objects between 45 cm and infinity. The camera is focused by rotating the lens, which moves it on the camera body and changes its distance from the film. In what range of distances between the lens and the film plane must the lens move to focus properly over the 45 cm to infinity range?
6 mm
Five moles of an ideal monatomic gas with an initial temperature of 127 C expand and, in the process, absorb 1200 J of heat and do 2100 J of work. What is the final temperature of the gas?
113 C.
A 1.20-cm-tall object is 50.0 cm to the left of a converging lens of focal length 40.0 cm. A second converging lens, this one having a focal length of 60.0 cm, is located 300.0 cm to the right of the first lens along the same optic axis. (a) Find the location and height of the image (call it I1) formed by the lens with a focal length of 40.0 cm. (b) I1 is now the object for the second lens. Find the location and height of the image produced by the second lens. This is the final image produced by the combination of lenses
(a) 200 cm to the right of lens 1, 4.80 cm tall and inverted.
(b) 150 cm to the right of lens 2, 7.20 cm tall and upright.
Monochromatic light from a distant source is incident on a slit 0.750 mm wide. On a screen 2.00 m away, the distance from the central maximum of the diffraction pattern to the first minimum is measured to be 1.35 mm. Calculate the wavelength of the light.
506 nm
A photographic slide is to the left of a lens. The lens projects an image of the slide onto a wall 6.00 m to the right of the slide. The image is 80.0 times the size of the slide. Is the lens converging or diverging?
f = 0.0632 m, hence the lens is converging.
When a camera is focused, the lens is moved away from or toward the film. If you take a picture of your friend, who is standing 3.90 m from the lens, using a camera with a lens with a 85-mm focal length, how far from the film is the lens? Will the whole image of your friend, who is 175 cm tall, fit on film that is 24 x 36 mm?
s' = 0.0869 m
y' = (-)39.0 mm
Your friend is too tall! Move further away from him to take a picture.
The Humber Bridge in England has the world’s longest single span, 1410 m. Calculate the change in length of the steel deck of the span when the temperature increases from -5.0 Celsius to 18.0 Celsius. For steel, the thermal expansion coefficient is 1.2 x 10^(-5).
+0.39 m
A 1.20-cm-tall object is 50.0 cm to the left of a converging lens of focal length 40.0 cm. A second diverging lens, this one having a focal length of 60.0 cm, is located 300.0 cm to the right of the first lens along the same optic axis. Find the location and height of the image produced by the second lens. This is the final image produced by the combination of lenses.
37.5 cm to the left of the second lens, 1.80 cm tall and inverted.
Monochromatic light with wavelength 620 nm passes through a circular aperture with diameter The resulting diffraction pattern is observed on a screen that is 4.5 m from the aperture.
theta = 0.102 rad
A converging lens with a focal length of 90.0 cm forms an image of a 3.20-cm-tall real object that is to the left of the lens. The image is 4.50 cm tall and inverted. Where are the object and image located in relation to the lens?
The object is 154 cm to the left of the lens. The image is 217 cm to the right of the lens and is real.
Where is the near point of an eye for which a contact lens with a power of +2.75 D (diopters) is prescribed.
NP = 80 cm
A 500.0-g chunk of an unknown metal, which has been in boiling water (100 Celsius) for several minutes, is quickly dropped into an insulating Styrofoam beaker containing 1.00 kg of water at 20 Celsius. After waiting and gently stirring for 5.00 minutes, you observe that the water’s temperature has reached a constant value of 22.0 Celsius. Assuming that the Styrofoam absorbs a negligibly small amount of heat and that no heat was lost to the surroundings, what is the specific heat of the metal?
*specific heat of water is 4190 J/(kg*K)
c_metal = 215 J/(kg*K)
Two thin lenses with a focal length of magnitude 12.0 cm, the first diverging and the second converging, are located 9.00 cm apart. An object 2.50 mm tall is placed 20.0 cm to the left of the first (diverging) lens. What is the height of the final image? Is it upright or inverted?
h = 2.50 mm and inverted.
Although we have discussed single-slit diffraction only for a slit, a similar result holds when light bends around a straight, thin object, such as a strand of hair. From actual laboratory measurements on a human hair, it was found that when a beam of light of wavelength 632.8 nm was shone on a single strand of hair, and the diffracted light was viewed on a screen 1.25 m away, the first dark fringes on either side of the central bright spot were 5.22 cm apart. How thick was this strand of hair?
30.2 micrometers
A converging lens forms an image of an 8.00-mm-tall real object. The image is 12.0 cm to the left of the lens, 3.40 cm tall, and erect. What is the focal length of the lens?
f = 3.69 cm
The picture size on ordinary 35-mm camera film is 24 x 36 mm. Focal lengths of lenses available for 35-mm cameras typically include 28, 35, 50 (the “normal” lens), 85, 100, 135, 200, and 300 mm. Which of these lenses should be used to photograph a building 240 m tall and 160 m wide at a distance of 600 m (assuming that the object is to fill most of the picture area).
f = 85 mm lens
Two loudspeakers, A and B emit sinusoidal waves of the same frequency in phase. Speaker B is 2.00 m directly to the right of speaker A. Consider point Q along the extension of the line connecting the speakers, 1.00 m to the right of speaker B. What is the lowest frequency for which constructive interference occurs at point Q?
172 Hz