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Light and optics exercises · Physics Playground

ExercisesPhysics

Light and optics

43 problems with worked solutions, from Physics and College Physics.

Start with a random one

Learn it first: Reflection & Refraction, Lenses & Images, Interference: Light as a Wave

Physics15.2 The Behavior of Electromagnetic Radiation

ExampleFrequency and Wavelength CalculationFor example, you can calculate the frequency of yellow light with a wavelength of 6.00× 10 ^(−7) m.
ExampleCalculating IlluminanceA woman puts a new bulb in a floor lamp beside an easy chair. If the luminous flux of the bulb is rated at 2,000 lm, what is the illuminance on a book held 2.00 m from the bulb?

Physics16.1 Reflection

ExampleCalculating Focal LengthA person standing 6.0 m from a convex security mirror forms a virtual image that appears to be 1.0 m behind the mirror. What is the focal length of the mirror?
ExampleCalculating Object DistanceElectric room heaters use a concave mirror to reflect infrared (IR) radiation from hot coils. Note that IR radiation follows the same law of reflection as visible light. Given that the mirror has a radius of…

Physics16.2 Refraction

ExampleCalculating Index of Refraction from SpeedCalculate the index of refraction for a solid medium in which the speed of light is 2.012 × 108 m/s, and identify the most likely substance, based on the previous table of indicies of refraction.
ExampleCalculating Index of Refraction from AnglesSuppose you have an unknown, clear solid substance immersed in water and you wish to identify it by finding its index of refraction. You arrange to have a beam of light enter it at an angle of 45.00°, and you observe…
ExampleCalculating Critical AngleVerify that the critical angle for light going from water to air is 48.6°. (See Table 16.2, the table of indices of refraction.)

Physics16.3 Lenses

ExampleImage Formation by a Convex LensA clear glass light bulb is placed 0.75 m from a convex lens with a 0.50 m focal length, as shown in Figure 16.36. Use ray tracing to get an approximate location for the image. Then, use the mirror/lens equations to…With a figure
ExampleImage Formation by a Concave LensSuppose an object, such as a book page, is held 6.50 cm from a concave lens with a focal length of –10.0 cm. Such a lens could be used in eyeglasses to correct pronounced nearsightedness. What magnification is produced?

Physics17.1 Understanding Diffraction and Interference

ExampleTwo-Slit InterferenceSuppose you pass light from a He-Ne laser through two slits separated by 0.0100 mm, and you find that the third bright line on a screen is formed at an angle of 10.95º relative to the incident beam. What is the…
ExampleSingle-Slit DiffractionVisible light of wavelength 550 nm falls on a single slit and produces its second diffraction minimum at an angle of 45.0° relative to the incident direction of the light. What is the width of the slit?

Physics17.2 Applications of Diffraction, Interference, and Coherence

ExampleChange of WavelengthA monochromatic laser beam of green light with a wavelength of 550 nm passes from air to water. The refractive index of water is 1.33. What will be the wavelength of the light after it enters the water?
ExampleDiffraction GratingA diffraction grating has 2000 lines per centimeter. At what angle will the first-order maximum form for green light with a wavelength of 520 nm?
ExampleResolutionWhat is the minimum angular spread of a 633-nm-wavelength He-Ne laser beam that is originally 1.00 mm in diameter?

College Physics24.2 Production of Electromagnetic Waves

Example 24.1Calculating B-Field Strength in an Electromagnetic WaveWhat is the maximum strength of the B-field in an electromagnetic wave that has a maximum E-field strength of 1000 V/m?

College Physics24.3 The Electromagnetic Spectrum

Example 24.2Calculating Wavelengths of Radio WavesCalculate the wavelengths of a 1530-kHz AM radio signal, a 105.1-MHz FM radio signal, and a 1.90-GHz cell phone signal.
Example 24.3Integrated Concept Problem: Correcting Vision with LasersDuring laser vision correction, a brief burst of 193-nm ultraviolet light is projected onto the cornea of a patient. It makes a spot 0.80 mm in diameter and evaporates a layer of cornea 0.30μm thick. Calculate the…

College Physics24.4 Energy in Electromagnetic Waves

Example 24.4Calculate Microwave Intensities and FieldsOn its highest power setting, a certain microwave oven projects 1.00 kW of microwaves onto a 30.0 by 40.0 cm area. (a) What is the intensity in W/m^2? (b) Calculate the peak electric field strength E0 in these waves.…

College Physics25.3 The Law of Refraction

Example 25.1Speed of Light in MatterCalculate the speed of light in zircon, a material used in jewelry to imitate diamond.
Example 25.2Determine the Index of Refraction from Refraction DataFind the index of refraction for medium 2 in Figure 25.12(a), assuming medium 1 is air and given the incident angle is 30.0º and the angle of refraction is 22.0º.
Example 25.3A Larger Change in DirectionSuppose that in a situation like that in Example 25.2, light goes from air to diamond and that the incident angle is 30.0º. Calculate the angle of refraction θ2 in the diamond.

College Physics25.4 Total Internal Reflection

Example 25.4How Big is the Critical Angle Here?What is the critical angle for light traveling in a polystyrene (a type of plastic) pipe surrounded by air?

College Physics25.6 Image Formation by Lenses

Example 25.5What is the Power of a Common Magnifying Glass?Suppose you take a magnifying glass out on a sunny day and you find that it concentrates sunlight to a small spot 8.00 cm away from the lens. What are the focal length and power of the lens?
Example 25.6Finding the Image of a Light Bulb Filament by Ray Tracing and by the Thin Lens EquationsA clear glass light bulb is placed 0.750 m from a convex lens having a 0.500 m focal length, as shown in Figure 25.35. Use ray tracing to get an approximate location for the image. Then use the thin lens equations to…With a figure
Example 25.7Image Produced by a Magnifying GlassSuppose the book page in Figure 25.37 (a) is held 7.50 cm from a convex lens of focal length 10.0 cm, such as a typical magnifying glass might have. What magnification is produced?
Example 25.8Image Produced by a Concave LensSuppose an object such as a book page is held 7.50 cm from a concave lens of focal length –10.0 cm. Such a lens could be used in eyeglasses to correct pronounced nearsightedness. What magnification is produced?

College Physics25.7 Image Formation by Mirrors

Example 25.9A Concave ReflectorElectric room heaters use a concave mirror to reflect infrared (IR) radiation from hot coils. Note that IR follows the same law of reflection as visible light. Given that the mirror has a radius of curvature of 50.0…
Example 25.10Solar Electric Generating SystemOne of the solar technologies used today for generating electricity is a device (called a parabolic trough or concentrating collector) that concentrates the sunlight onto a blackened pipe that contains a fluid. This…
Example 25.11Image in a Convex MirrorA keratometer is a device used to measure the curvature of the cornea, particularly for fitting contact lenses. Light is reflected from the cornea, which acts like a convex mirror, and the keratometer measures the…

College Physics26.1 Physics of the Eye

Example 26.1Size of Image on RetinaWhat is the size of the image on the retina of a 1.20×10^(−2) cm diameter human hair, held at arm’s length (60.0 cm) away? Take the lens-to-retina distance to be 2.00 cm.
Example 26.2Power Range of the EyeCalculate the power of the eye when viewing objects at the greatest and smallest distances possible with normal vision, assuming a lens-to-retina distance of 2.00 cm (a typical value).

College Physics26.2 Vision Correction

Example 26.3Correcting NearsightednessWhat power of spectacle lens is needed to correct the vision of a nearsighted person whose far point is 30.0 cm? Assume the spectacle (corrective) lens is held 1.50 cm away from the eye by eyeglass frames.
Example 26.4Correcting FarsightednessWhat power of spectacle lens is needed to allow a farsighted person, whose near point is 1.00 m, to see an object clearly that is 25.0 cm away? Assume the spectacle (corrective) lens is held 1.50 cm away from the eye…

College Physics26.4 Microscopes

Example 26.5Microscope MagnificationCalculate the magnification of an object placed 6.20 mm from a compound microscope that has a 6.00 mm focal length objective and a 50.0 mm focal length eyepiece. The objective and eyepiece are separated by 23.0 cm.

College Physics27.3 Young’s Double Slit Experiment

Example 27.1Finding a Wavelength from an Interference PatternSuppose you pass light from a He-Ne laser through two slits separated by 0.0100 mm and find that the third bright line on a screen is formed at an angle of 10.95º relative to the incident beam. What is the wavelength…
Example 27.2Calculating Highest Order PossibleInterference patterns do not have an infinite number of lines, since there is a limit to how big m can be. What is the highest-order constructive interference possible with the system described in the preceding example?

College Physics27.4 Multiple Slit Diffraction

Example 27.3Calculating Typical Diffraction Grating EffectsDiffraction gratings with 10,000 lines per centimeter are readily available. Suppose you have one, and you send a beam of white light through it to a screen 2.00 m away. (a) Find the angles for the first-order…With a figure

College Physics27.5 Single Slit Diffraction

Example 27.4Calculating Single Slit DiffractionVisible light of wavelength 550 nm falls on a single slit and produces its second diffraction minimum at an angle of 45.0º relative to the incident direction of the light. (a) What is the width of the slit? (b) At…With a figure

College Physics27.6 Limits of Resolution: The Rayleigh Criterion

Example 27.5Calculating Diffraction Limits of the Hubble Space TelescopeThe primary mirror of the orbiting Hubble Space Telescope has a diameter of 2.40 m. Being in orbit, this telescope avoids the degrading effects of atmospheric distortion on its resolution. (a) What is the angle…

College Physics27.7 Thin Film Interference

Example 27.6Calculating Non-reflective Lens Coating Using Thin Film InterferenceSophisticated cameras use a series of several lenses. Light can reflect from the surfaces of these various lenses and degrade image clarity. To limit these reflections, lenses are coated with a thin layer of…
Example 27.7Soap Bubbles: More Than One Thickness can be Constructive(a) What are the three smallest thicknesses of a soap bubble that produce constructive interference for red light with a wavelength of 650 nm? The index of refraction of soap is taken to be the same as that of water.…

College Physics27.8 Polarization

Example 27.8Calculating Intensity Reduction by a Polarizing FilterWhat angle is needed between the direction of polarized light and the axis of a polarizing filter to reduce its intensity by 90.0%?
Example 27.9Calculating Polarization by Reflection(a) At what angle will light traveling in air be completely polarized horizontally when reflected from water? (b) From glass?