# Calculate distances and focal lengths using the mirror equation for concave and convex spherical mirrors.…

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Real vs. Virtual Images  A real image is an image formed when rays of light actually converge and pass through a point on the image. Real images can be projected onto a screen.  Virtual images are behind a plane mirror The rays reflected never actually converge but appear to diverge from behind the mirror

### Text of Calculate distances and focal lengths using the mirror equation for concave and convex spherical...

Calculate distances and focal lengths using the mirror equation for concave and convex spherical mirrors.

Draw ray diagrams to find the image distance and magnification for concave and convex spherical mirrors.

Distinguish between real and virtual images.

Differentiate between parabolic mirrors andspherical mirrors.

Concave Mirrors

A concave spherical mirror is a mirror whose reflecting surface is a segment of the inside of a sphere.Reflects light from its inner caved in surfaceConcave mirrors can be used to form real images.

Real vs. Virtual Images

A real image is an image formed when rays of light actually converge and pass through a point on the image. Real images can be projected onto a screen.Virtual images are behind a plane mirrorThe rays reflected never actually converge but appear to diverge from behind the mirror

The radius of curvature, R, is one factor that determines the size and where the image will appear R is the distance from the mirrors surface to the center of curvature, CC is the geometric center of the spherePrinciple axis is the straight line perpendicular to the center of the surface of the mirror

F is the focal point: where the reflected rays cross the principal axis; parallel rays converge at Ff is the focal length of the mirror which is the distance from F to the mirror along the principal axis2f=R

Locating images in mirrors by ray tracing

Determine scale of drawing

If object is beyond F, then image will be on object side of mirror. Draw mirror on right side of paper

If the object is beyond C, the image distance will be small, so draw object near left side of paper

If object is between C and F, the image will be beyond C. The closer the object is to F, the farther away the image will be, so image will be near left side of paper

Draw the principal axis.

Draw vertical line where principal axis touches mirror.

If the focal point is known, indicate that position on the principal axis and label it F.

Identify and label center of curvature, C (it is twice the focal distance, f, from mirror)

Draw object

Draw ray 1 from top of object parallel to principal axis. (All rays parallel to principal axis are reflected through F)

Draw ray 2 from top of object through F. (It will be reflected parallel to principal axis)

Draw ray 3 from top of object through C.

The image is located where any two rays intersect. The third ray is used to check. Draw line to principal axis to represent image

Practice Problem

The focal length is 20.0 cm. Draw a ray diagram to identify where each image is formed.

Object is at C

Object is at F

Object is between C and F

Object outside C

Object inside F

You can use the mirror equation below to predict the image location.p and q have a positive value if they are on the front side or reflecting side of the mirror.Real imagesq has a negative value if the image is on the back side of the mirror.Virtual imagef is positive for concave mirrors.

h is positive if it is upright and negative when inverted.M is positive for virtual (upright) images and negative for inverted images.Geometry shows that the ratio between image and object height is the same as the ratio between image and object distance. The negative sign is required because images on the back side of the mirror have negative image distances.

Practice problem

A concave spherical mirror has a focal length of 10.0 cm. Locate the image of a pencil that is placed upright 30.0 cm from the mirror. Find the magnification of the image. Draw a ray diagram reference.

Spherical aberration

With spherical mirrors, rays not near the principal axis do not all meet at the image point (spherical aberration, which causes blurry images)Parabolic mirrors eliminate this problem and produce sharper images

(reflecting telescopes).

Paraxial rays are very near the principal axis, make the assumption that all the rays in drawings and calculations are paraxial even if they may not appear to be.

Convex Mirrors

Spherical mirror whose reflecting surface is outward-curved segment of a sphere Also called diverging mirror Reflected rays spread outSide-view mirrors on carsImage is always virtual and smaller than objectAppears to be farther awayObjects may be closer than they actually appear

Convex Ray Diagrams

F is behind the mirrorStill half way between C and mirrorIf using mirror equations, f is negative, image distance is also negative

Convex Ray Diagrams

Ray 1: from top of object parallel to principal axisReflected ray: draw dashed line from F to point where ray 1 strikes mirror, continue line past mirrorRay 2: approaches mirror on a path that, if extended behind mirror, would pass through FReflected ray: parallel to principal axis, continue it behind mirror.

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