Unit 13: Geometric Optics
Light traced as straight rays that bend at a boundary, bounce off a curve, and come together into an image you can locate with one equation, no drawing needed.
14 topics · 50 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
The Speed of Light and the Index of Refraction
- How it worksHow does a material's index of refraction measure exactly how much it slows light down?
- Worked exampleFind the speed of light inside a piece of glass with an index of refraction of 1.5.
- Going furtherWhat happens to a material's index of refraction as that material slows light down even further?
Your turn1 of 2
Find the speed of light inside a material with an index of refraction of 21 times 0.1. Use c = 3x108 m/s.The Law of Reflection
- How it worksHow does the law of reflection set the reflected ray's angle equal to the incoming ray's, both from the normal?
- Worked exampleFind the angle of reflection of a light ray striking a flat mirror at 35 degrees from the normal.
- Common mistakeWhy isn't the angle of reflection measured from the mirror's own surface instead of from its normal line?
Your turn1 of 2
Write the angle of reflection off a flat mirror as a function of theta, the angle of incidence in degrees, both measured from the normal.Images in a Plane Mirror
- How it worksHow do reflected rays that never actually meet behind the mirror still form a real-looking virtual image there?
- Common mistakeWhy doesn't a plane mirror's image actually exist as light rays truly converging behind the glass?
- Ties togetherHow does a plane mirror's virtual, upright, same-size image set the baseline for comparing every curved mirror?
Your turn1 of 2
Write how far behind a flat mirror an image appears, as a function of d, the object's distance in front of the mirror.Snell's Law of Refraction
- How it worksHow does the direction light bends toward or away from the normal depend on which medium it's entering?
- Worked exampleFind the angle of refraction when light enters water at 40 degrees from air, given water's index is 1.33.
- Worked exampleFind the angle of incidence in air needed to produce a 20 degree angle of refraction inside glass of index 1.5.
- Common mistakeWhy doesn't light bend at all the moment it enters a new medium exactly along the normal?
Your turn1 of 2
Find the angle of refraction when light enters a medium of index 162 times 0.01 at 55 degrees from air (index 1).Total Internal Reflection
- How it worksHow does light striking an interface beyond the critical angle get reflected entirely instead of partly refracting through?
- Worked exampleFind the critical angle for light traveling from water, index 1.33, into air.
- How it worksWalk me through how total internal reflection lets an optical fiber trap light and guide it around bends.
- Going furtherWhat happens to the critical angle if light tries to pass from a higher-index medium into an even higher one?
- How it worksHow does total internal reflection guarantee that zero light escapes through the interface once the angle passes critical?
Your turn1 of 2
Find the critical angle for light traveling from a medium of index 173 times 0.01 into air (index 1).Dispersion and Prisms
- How it worksHow does a material's index of refraction depending slightly on wavelength bend different colors by different amounts?
- Worked exampleFind which color bends more passing through a prism, violet or red light, given violet's higher index in glass.
- Going furtherWhat happens to a prism's spread of colors if the glass is replaced with one whose index barely depends on wavelength?
Your turn1 of 2
A prism has an index of 158 times 0.01 for violet light and 150 times 0.01 for red light. Both colors enter the same face at 47 degrees from air. Find the difference between their angles of refraction (red's angle minus violet's angle).Ray Diagrams for Curved Mirrors
- How it worksHow do three principal rays traced from an object's tip let you locate its image in a concave mirror?
- How it worksWalk me through tracing those same three principal rays to find the image formed by a convex mirror instead.
- Common mistakeWhy can a convex mirror never form a real, inverted image no matter where its object is placed?
- Going furtherWhat happens to a concave mirror's image as the object crosses from beyond the focal point to inside it?
Your turn1 of 2
Is a convex, diverging mirror's image always virtual, upright, and reduced, no matter where the object is placed?The Mirror Equation
- How it worksHow do the object distance, image distance, and focal length fit together in the mirror equation?
- Worked exampleFind the image distance for an object 30 cm from a concave mirror with a focal length of 10 cm.
- Worked exampleFind that same image's magnification and state whether it comes out upright or inverted.
- Common mistakeWhy does a negative image distance in the mirror equation just mean a virtual image, not that something went wrong?
Your turn1 of 2
Find the image distance for an object 74 cm from a concave mirror with a focal length of 10 cm.Refraction at a Single Spherical Surface
- How it worksHow does light bending at a single curved interface between two media form an image with no lens involved?
- Worked exampleFind the image distance for an object 40 cm from a spherical glass surface of radius 20 cm separating air from glass of index 1.5.
- Ties togetherHow does refraction at one spherical surface become the building block for understanding a full lens later on?
Your turn1 of 2
Find the image distance for an object 88 cm from a spherical glass surface of radius 11 cm separating air (index 1) from glass of index 159 times 0.01.Ray Diagrams for Thin Lenses
- How it worksHow do three principal rays traced through a converging lens let you locate the image of an object?
- How it worksWalk me through tracing those same three principal rays through a diverging lens instead.
- Common mistakeWhy can a simple diverging lens never form a real image no matter how far its object sits away?
- Going furtherWhat happens to a converging lens's image as the object moves from far away to just past the focal point?
Your turn1 of 2
What kind of image does a simple diverging, concave lens form, and how does that depend on how far away the object is placed?The Thin-Lens Equation
- How it worksHow do object distance, image distance, and focal length combine in the thin-lens equation?
- Worked exampleFind the image distance for an object 15 cm from a converging lens with a focal length of 10 cm.
- Worked exampleFind where two 20 cm focal length lenses, 50 cm apart, form the final image of an object 30 cm in front of the first.
- Ties togetherHow does combining two lenses this way anticipate the way a microscope or telescope stacks lenses to magnify?
Your turn1 of 2
A converging lens has focal length 10 cm. Write the image distance as a function of do, the object distance in cm.The Human Eye as an Optical Instrument
- How it worksHow does the eye's own lens change shape to focus objects at different distances onto the retina?
- Common mistakeWhy doesn't nearsightedness mean the eye's lens is too weak, when the real problem is the eye being too long?
- Going furtherWhat happens to the light path through a nearsighted eye once a corrective lens is placed in front of it?
Your turn1 of 2
A nearsighted person's uncorrected far point is d cm. Write the focal length of the diverging corrective lens needed to let them see clearly at infinity, as a function of d.The Simple Magnifier
- How it worksHow does placing an object just inside a lens's focal length produce a magnified virtual image you can view comfortably?
- Worked exampleFind the angular magnification of a simple magnifier with a focal length of 5 cm, using a near point of 25 cm.
- Going furtherWhat happens to a simple magnifier's angular magnification as its own focal length is made shorter?
Your turn1 of 2
Find the angular magnification of a simple magnifier with a focal length of 11 cm, using a near point of 26 cm.Microscopes and Telescopes
- How it worksHow does a microscope's objective lens form a real image that its eyepiece then magnifies again as a simple magnifier?
- How it worksWalk me through how a refracting telescope uses a large objective lens and a small eyepiece to gather and magnify light from far away.
- Worked exampleFind the overall magnification of a compound microscope with an objective magnification of 40 and an eyepiece magnification of 10.
- Ties togetherHow do both the microscope and the telescope reuse the same image-then-magnify idea from the simple magnifier?
Your turn1 of 2
Find the overall magnification of a compound microscope with an objective magnification of 71 and an eyepiece magnification of 14.