# Optics: Twelve problems on different properties of light.

1. A dentist uses a mirror to examine a tooth that is 1.00 cm in front of the mirror. The image of the tooth is formed 10.0 cm behind the mirror. Determine (a) the mirror's radius of curvature and (b) the magnification of the image.

2. An object is placed 40.0 cm from a concave mirror of radius 20.0 cm. (a) Find the location of the image. (b) What is the magnification of the mirror? Is the image real or virtual? Is the image real or virtual? Is the image upright or inverted?

3. A concave makeup mirror is designed so that a person 25 cm in front of it sees an upright image magnified by a factor of two. What is the radius of curvature of the mirror?

4. A man standing 1.52 m in front of a shaving mirror produces an inverted image 18.0 cm in front of it. How close to the mirror should he stand if he wants to form an upright image of his chin that is twice the chin's actual size?

5. A converging lens has a focal length of 10.0 cm. Locate the images for object distances of (a) 20.0 cm, (b) 10.0 cm, and (c) 5.00 cm, if they exist. For each case, state whether the image is real or virtual, upright or inverted, and find the magnification.

6. A diverging lens has a focal length of 20.0 cm. Locate the images for object distances of (a) 40.0 cm, (b) 20.0 cm, and (c) 10.0 cm. For each case, state whether the image is real or virtual and upright or inverted, and find the magnification.

7. A laser beam is incident on two slits with a separation of 0.200 mm, and a screen is placed 5.00 m from the slits. If the bright interference fringes on the screen are separated by 1.58 cm, what is the wavelength of the laser light?

8. Light of wavelength 5.30 x 10^2 nm illuminates a pair of slits separated by 0.300 mm. If screen is placed 2.00 m from the slits, determine the distance between the first and second dark fringes.

9. A Young's double-slit interference experiment is performed with blue-green argon laser light. The separation between the slits is 0.500 mm, and the screen is located 3.30 m from the slits. The first bright fringe is located 3.40 mm from the center of the interference pattern. What is the wavelength of argon laser light?

10. A light source emits two major spectral lines: an orange line of wavelength 610 nm and a blue-green line of wavelength 480 nm. If the spectrum is resolved by a diffraction grating having 5000 lines/cm and viewed on a screen 2.00 m from the grating, what is the distance (in centimeters) between the two spectral lines in the second-order spectrum?

11. Light from an argon laser strikes a diffraction grating that has 5310 grooves per centimeter. The central and first-order principal maxima are separated by 0.488 m on a wall 1.72 m from the grating. Determine the wavelength of the laser light.

12. Does your bathroom mirror show you older or younger than your actual age? Compute an order-of-magnitude estimate for the age of difference.

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#### Solution Preview

Please see the attached.

12 Physics Questions

Redding:

The object distance q the image distance p and the focal length for a mirror is related as

The sign convention is

1. All distances are measured from the optical center of the lens or pole (vertex) of the mirror.

2. The distances measured in the direction of the incident rays are taken positive and in the direction opposite to that of incident rays are taken negative.

3. The lengths (object or image) measured above the principle axis are taken positive and in lower half plane are negative.

4. The focal length of converging lens is positive.

As the focus point F of the concave mirror is in front of the mirror its focal length OF = f will be negative.

As the rays are coming from a real source the object distance will be opposite to the incident ray and thus should be taken negative.

1. A dentist uses a mirror to examine a tooth that is 1.00 cm in front of the mirror. The image of the tooth is formed 10.0 cm behind the mirror. Determine (a) the mirror's radius of curvature and (b) the magnification of the image.

Here the object distance is q = - 1 cm

The image is behind the mirror thus p = + 10 cm

(a) Thus the focal length of the mirror is given by

Or

Or

Gives f = - 10/9 = - 1.11 cm

As the focal length of a mirror is half of the radius of curvature, we get radius of curvature of the mirror as

R = 2f = 2*(-1.11) = - 2.22 cm.

Thus the radius of curvature of the mirror is 2.22 cm.

(The negative sing shows that it is a concave mirror)

(b) The magnification m of an image for a mirror is given by

Hence substituting the values we get

(The positive sign is due to the image is erect.)

2. An object is placed 40.0 cm from a concave mirror of radius 20.0 cm. (a) Find the location of the image. ...

#### Solution Summary

Twelve problems related to reflection, reflection, interference, dispersion are solved and explained.

10 problems about light, wave length, focal length, telescope, polarized beam

(Please refer to the attachment for detailed description of the problems)

1. An object is placed 30 cm to the left of a converging lens of focal length f1= + 20 cm. A second lens sits 40 cm to the right of the first lens. The two- lens system produces an overall magnification of M= + 2.0. What is the focal length (f2) of the second lens?

2. A person looks straight ahead at the left-hand edge of a 1.0m wide mirror mounted on the wall in front of them (see the diagram below). If the person is standing 3.0maway from the mirrored wall and 4.0mfromawall behind them, what length of the wall behind them is visible in the mirror?

3. You are given an eyepiece lens of focal length fe= +5.0 cm and a paper towel tube, 28.0 cm in length. a. What focal length would you need for the objective lens to make an astronomical telescope? b. What is the telescope's magnification for a relaxed eye?

4. A microscope of length L = 12.0 cm has a 33× eyepiece lens. If the objective lens has a focal length of 1.1 cm, find the overall magnification of the microscope. Assume a normal relaxed eye.

5. 5. Monochromatic light of wavelength1 = 500 nm falls on two narrow slits. A first order (m= 1) maximum is detected at an angle of 5.3from the Central maximum on a screen, 1.8maway. If the light source is changed to

2 = 630 nm, what distance does them= 1maximum move on the screen?

6. A single slit illuminated by light of wavelength 610 nm produces a diffraction pattern with its first minimum at 3.5 mm from the central maximum.

a) Find the slit width, (b) wavelength of light used (Λ)=610nm=610*10-9m

7. A light beam in air is incident on a glass surface at an angle of 60.00. The narrow beam contains both blue light that travels at a speed of 2.023 × 108m/s in the glass, and red light that travels at 2.034 × 108 m/s. Assume both colours travel at c = 2.998 × 108 m/s in air. How far must the blue and red beams travel in the glass before they are separated by 1.0 cm?

8. The line spectrum of sodium includes a yellow line with 1 = 589.00 nm. A certain diffraction grating produces this line, in first order, at1 = 25.00 from the central maximum. A second distinct line has2 = 589.59 nm. What is the angular separation between these two lines?

9. Light passes through a first polaroid, producing a beam of intensity Io that is 100% polarized in the vertical direction. The beam then passes through a second polaroid with axis at 30 to the vertical, and a third polaroid at 90 degrees to the vertical. What fraction of Io emerges from the three polaroids?

10. Atoms in a crystal are spaced d = 0.145 nm apart, forming an exactly square lattice. When x- rays of wave length = 0.100 nm strike the horizontal planes of atoms, as shown in the diagram below, diffraction maxima are formed at certain angles. In addition, atoms joined by the diagonal line also form planes and produce maxima. Ifis varied from 0to 90, find the angles where diffraction maxima are produced by the diagonal (dashed) plane.

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