An image is being formed by a mirror with a spherical radius of R=+40cm. Draw mirror spherical surface curving to the right!

Transcription

1 Image formation by Reflection at a Spherical Mirror An image is being formed by a mirror with a spherical radius of R=+40cm. Left side of room: Right side of room: Draw mirror spherical surface curving to the left! Draw mirror spherical surface curving to the right! Spherical Mirror urving to the Left Spherical Mirror urving to the Right Answer these four questions / do these four tasks first: 1) On which side of mirror is the sphere s center? Draw! Hint: Which way does your mirror curve? A: See drawings on last three pages, below. Think of the curved mirror surface as part of a complete sphere: Where is the center,, of that sphere? or left-curving mirror, is to the left of mirror. or right-curving mirror, is to the right of mirror. 2) Which side of the mirror is its outgoing side? Mark it as. Hint: Use, sign of R and sign convention for R. A: Radius R is positive and, by sign convention, is on the outgoing side if R>0. Thus: or left-curving mirror, outgoing side is to the left of mirror. or right-curving mirror, outgoing side is to the right of mirror. Note: A mirror with R>0 is also called a concave or also a convergent mirror. A mirror with R<0 would be called a convex or also a divergent mirror.

2 3) Which side of the mirror is its incoming side? Mark it as. Hint: It s a mirror à incoming rays are reflected to produce outgoing rays. A: The mirror reflects the incoming rays to produce the outgoing rays. The outgoing rays are thus traveling away from the mirror towards the same side from which the incoming rays are striking the mirror. So, for a mirror, the incoming side is always the same as the outgoing side (regardless of the sign of R!) and hence: or left-curving mirror, incoming side is to the left of mirror. or right-curving mirror, incoming side is to the right of mirror. 4) On which side of mirror is the ect being placed? Draw ect as upright arrow. Hint: Use sign of d and sign convention for d. All d-values given in the input table are positive. By sign convention for d, the oject must be on the incoming side if d>0, and hence: or left-curving mirror, ect is to the left of mirror. or right-curving mirror, ect is to the right of mirror. Then calculate d, m, h, for all d-values shown in the table below and do the following for each of these four d-values, d=15cm, d=25cm, d=40cm, d=60cm : 5) Draw the image on the correct side of the mirror: to the left or the right of mirror? Draw the image with the correct orientation: erect or inverted? Draw the image at correct position rel. to ect: to the left or the right of ect? Hints: --Use the sign convention for d and the marking from 2) to figure out where the image is located relative to the mirror: to the left or to the right? --Use the sign convention for m to figure out how the image is oriented relative to the ect: erect or inverted? --Use the relative magnitude of d and d to figure out which is closer to the mirror: ect or image? rom that and from the positioning of ect and image relative to the mirror, figure out whether the image is to the left or the right of the ect. A: See the drawings and the table for d, m, h on pages below and note the following to understand how the drawings were made for each of the four d-values listed:

3 a) or d=15cm à d =-60cm, m=+4.0. d <0 à by d -sign-convention, image is not on outgoing side or left-curving mirror, outgoing side = left of mirror à image to right of mirror or right-curving mirror, outgoing side = right of mirror à image to left of mirror m>0 à by m-sign-convention, image is erect, for either left- or right-curving mirror. Image and ect are on opposite sides of the mirror, for both left- and right-curving mirror. Hence: or left-curving mirror, outgoing side = left of mirror à image to right of ect or right-curving mirror, outgoing side = right of mirror à image to left of ect b) or d=25cm à d =+100cm, m=-4.0. d >0 à by d -sign-convention, image is on outgoing side or left-curving mirror, outgoing side = left of mirror à image to left of mirror or right-curving mirror, outgoing side = right of mirror à image to right of mirror m<0 à by m-sign-convention, image is inverted, for either left- or right-curving mirror. Image and ect are on same side of the mirror, for both left- and right-curving mirror. Also, d > d means that the image is further away from mirror than ect is from mirror. Hence, or left-curving mirror, image to left of ect or right-curving mirror, image to right of ect c) or d=40cm à d =+40cm, m=-1.0. d >0, m<0 à same as in b): or left-curving mirror, image to left of mirror or right-curving mirror, image to right of mirror or either left or right-curving mirror, image is inverted d = d à image and ect horizontal positions coincide on optical axis, for either left- or right-curving mirror.

4 d) or d=60cm à d =+30cm, m=-0.5. d >0, m<0 à same as in b): or left-curving mirror, image to left of mirror or right-curving mirror, image to right of mirror or either left or right-curving mirror, image is inverted Image and ect are on same side of the mirror, for either left- or right-curving mirror. Also, d < d means that the image is closer to mirror than ect is to mirror. Hence, or left-curving mirror, image to right of ect or right-curving mirror, image to left of ect

5 Image formation by Reflection at a Spherical Mirror d'= 1/ (1/f - 1/d) m := h'/h = -d' / d h' = m h h= 3 cm R= 40 cm <-- R > 0 f=r/2= 20 cm image virtual image inverted d [cm] d' [cm] m h' [cm] or real? or erect? virtual erect virtual erect virtual erect d~f, d<f virtual erect d~f, d>f real inverted real inverted real inverted d=r --> real inverted real inverted real inverted Sign conventions for d, d', R, m: d > 0 : ect on incoming side of device (real ect) d < 0 : ect not on incoming side of device (virtual ect) d' > 0 : image on outgoing side of device (real image) d' < 0 : image not on outgoing side of device (virtual image) R > 0 : R < 0 : m > 0 : m < 0 : center on outgoing side of device center not on outgoing side of device image upright(erect) rel. to ect image upside-down(inverted) rel. to ect

6 Mirror urving to the Left with R>0, d>0 Mirror urving to the Right with R>0, d>0

7 d = 15cm d =-60cm d = 25cm d = 100cm Mirror urving to the Left d = 40cm d = 40cm d = 60cm d = 30cm

8 d = 25cm d = 100cm d = 15cm d =-60cm Mirror urving to the Right d = 60cm d = 30cm d = 40cm d = 40cm