Reflection: Convex & Concave Lenses

Reflection: Convex & Concave Lenses Pay attention!

The Law of Refraction • Regardless of whether we are dealing with a concave (thinner at center) lens or a convex (thicker at center) lens, the law of refraction still holds… • na• sin(θa) = nb• sin(θb) … where θa is the angle of incidence from one medium and θa is the angle of refraction into a second medium

Let’s put the “fizz” back into Fizzics! • Let us first remember that all lenses have a focal point (F). • Positive F for convex (thicker at center) lenses, and negative F for concave (thinner at center) lenses. (Just the OPPOSITE of mirrors.) • The focal length (f) is equal to ½ the radius of curvature (R). This means f = ½R. • “R” measures from the center (C) of a circle to it’s surface. Thus F = ½C, which means 2F = C.

Convex Lenses • Have a “belly” since they are always thicker at center. • Usually converge light and thus have images appear on the side opposite to the object. • Convex lenses have a positive focus. concavo-convex biconvex plano-convex

An example… • 1st: Determine which focus to use: objects are ALWAYS positive, and images are positive on the side opposite to the object, so mark your positive and negative sides right away • 2nd: POA Principal Optic Axis : from the base of object through the Focus (F) and Center (C or 2F) to middle of lens • 3rd: From Head to lens: parallel to POA to middle of lens, and then through the focus of lens • 4th:From Head through middle of lens: as if refracted equally as straight line REMEMBER: It must go through POSITIVE focus since this is a convex lens! 2F – F + F 2F real because the image is on the positive side formed with converging rays inverted because the image points in the opposite direction larger real (positive) equal imaginary (negative) The image is thus… erect inverted smaller s v r

Another example… • 1st: Determine which focus to use: objects are ALWAYS positive, and images are positive on the side opposite to the object, so mark your positive and negative sides right away • 2nd: POA Principal Optic Axis : from the base of object through the Focus (F) and Center (C or 2F) to middle of lens • 3rd: From Head to lens: parallel to POA to middle of lens, and then through the focus of lens • 4th:From Head through middle of lens: as if refracted equally as straight line REMEMBER: It must go through POSITIVE focus since this is a convex lens! F C + – F C larger real because the image is on the positive side formed with converging rays inverted because the image points in the opposite direction equal real (positive) imaginary (negative) The image is thus… erect inverted smaller e v r

Another example… • 1st: Determine which focus to use: objects are ALWAYS positive, and images are positive on the side opposite to the object, so mark your positive and negative sides right away • 2nd: POA Principal Optic Axis : from the base of object through the Focus (F) and Center (C or 2F) to middle of lens • 3rd: From Head to lens: parallel to POA to middle of lens, and then through the focus of lens • 4th:From Head through middle of lens: as if refracted equally as straight line inverted because the image points in the opposite direction REMEMBER: It must go through POSITIVE focus since this is a convex lens! F C + – F C real because the image is on the positive side formed with converging rays larger equal real (positive) imaginary (negative) The image is thus… erect inverted smaller v r l

Last and unique example… • 1st: Determine which focus to use: objects are ALWAYS positive, and images are positive on the side opposite to the object, so mark your positive and negative sides right away • 2nd: POA Principal Optic Axis : from the base of object through the Focus (F) and Center (C or 2F) to middle of lens • 3rd: From Head to lens: parallel to POA to middle of lens, and then through the focus of lens • 4th:From Head through middle of lens: as if refracted equally as straight line REMEMBER: It must go through POSITIVE focus since this is a convex lens! F C + – F C larger imaginary because the image is on the negative side formed with virtual converging rays erect because the image points in the same direction NOTICE! The lines diverge and will NEVER meet. Therefore, draw them back to where they appear to meet. equal real (positive) imaginary (negative) The image is thus… erect inverted smaller l c i

Concave Lenses • Form a sort of “cave” since they are always thinner at center. • ALWAYS diverge light and thus have images appear on the same side as the object. • Convex lenses have a negative focus. plano-concave biconcave convexo-concave

An example… • 1st: Determine which focus to use: objects are ALWAYS positive, and images are positive on the side opposite to the object, so mark your positive and negative sides right away • 2nd: POA Principal Optic Axis : from the base of object through the Focus (F) and Center (C or 2F) to middle of lens • 3rd: From Head to lens: parallel to POA to middle of lens, and then through the focus of lens • 4th:From Head through middle of lens: as if refracted equally as straight line REMEMBER: It must go through NEGATIVE focus since this is a concave lens! But since the negative focus is BEHIND the ray, then it must APPEAR to come from that focus. F C + – F C The image is thus… s c i larger imaginary because the image is on the negative side formed with virtual converging rays erect because the image points in the same direction NOTICE! Concave rays always produce diverging rays. Therefore, they will ALWAYS produce smaller, erect and imaginary images REGARDLESS of where the object is located in relation to the focus, unlike converging (convex) lenses which can produce four different types of images. equal real (positive) imaginary (negative) erect inverted smaller

Another example… • 1st: Determine which focus to use: objects are ALWAYS positive, and images are positive on the side opposite to the object, so mark your positive and negative sides right away • 2nd: POA Principal Optic Axis : from the base of object through the Focus (F) and Center (C or 2F) to middle of lens • 3rd: From Head to lens: parallel to POA to middle of lens, and then through the focus of lens • 4th:From Head through middle of lens: as if refracted equally as straight line REMEMBER: It must go through NEGATIVE focus since this is a concave lens! But since the negative focus is BEHIND the ray, then it must APPEAR to come from that focus. F C + – F C The image is thus… s c i larger imaginary because the image is on the negative side formed with virtual converging rays erect because the image points in the same direction NOTICE! Concave rays always produce diverging rays. Therefore, they will ALWAYS produce smaller, erect and imaginary images REGARDLESS of where the object is located in relation to the focus. Notice that as you get closer to the lens, the images get larger. equal real (positive) imaginary (negative) erect inverted smaller

Another example… • 1st: Determine which focus to use: objects are ALWAYS positive, and images are positive on the side opposite to the object, so mark your positive and negative sides right away • 2nd: POA Principal Optic Axis : from the base of object through the Focus (F) and Center (C or 2F) to middle of lens • 3rd: From Head to lens: parallel to POA to middle of lens, and then through the focus of lens • 4th:From Head through middle of lens: as if refracted equally as straight line REMEMBER: It must go through NEGATIVE focus since this is a concave lens! But since the negative focus is BEHIND the ray, then it must APPEAR to come from that focus. F C + – F C The image is thus… s c i larger imaginary because the image is on the negative side formed with virtual converging rays erect because the image points in the same direction NOTICE! Unlike convex lenses which CANNOT produce images when an object is located at the focus, concavelenses WILL produce images, but they are virtual and get larger as you get closer to the lens. equal real (positive) imaginary (negative) erect inverted smaller

Reflection: Convex & Concave Lenses