Curved Mirrors problems?

1.) a.) If you look at yourself in a shiny Christmas tree ball with a diameter of 9.0 cm when your face is 24.0 cm away from it, where is your image (in meters from the ball's surface)? (Your answer should be positive if the image is in front of the ball's surface, and negative if the image is behind it.)


b.) Is it real or virtual?


c.) Is it upright or inverted?





2.) A mirror at an amusement park shows an upright image of any person who stands 1.8 m in front of it. If the image is three times the person's height, what is the radius of curvature (in meters)?





3.) a.) A dentist wants a small mirror that, when 2.70 cm from a tooth, will produce a 3.5X upright image. What kind of mirror must be used, a convex or concave mirror?


b.) What must its radius of curvature be (in centimeters)?





If you can only do one or a few of these problems, that is okay. I need all the help I can get... explanations would be nice, too. Thanks in advance.

Curved Mirrors problems?
Ok, let's go on with the problems :





1) We can consider, or we must consider the christmas ball as a convex mirror, then :





1 / p + 1 / q = 1 / f





p = object distance





q = image distance





f = focal distance ; R = 2f





The diameter of the ball is 9 cm, then : R = 4.5 cm





Then : F = 2.25 cm





Remember, that for a convex mirror, the focal distance is always negative, then :





1 / 24 + 1 / q = - 1 / 2.25





q = - 2.06





It's a virtual image, as you can see, the sing is negative, and it's 2.06, behind the mirror.





If the sign of "q" is negative, then the magnification is positive, we can say then that the image is upright.





2) Second problem :





Remember always : 1 / p + 1 / q = 1 / f





and also, magnification : m = - q / p





If the image is upright, the magnification is positive.





p = 1.18 m





q = three times "p" ; q = 3.54 m





But, the image is upright, then : q = - 3.54





1 / 1.18 - 1 / 3.54 = 1 / f





f = 1.77





f = R / 2





Radius = 3.54 meters





3) Classical problem of the dentist :





It's the same as the problem above, it's an upright image, so the sign of the " image distance : q ", will be negative.





p = 2.7 cm





q = 3.5p = 9.45, but, if the image is upright, then : q = -9.45





1 / 2.7 - 1 / 9.45 = 1 / f





f = 3.78 cm





He must use a concave mirro, with 7.56 cm of Radius.





That's it





Hope that helps

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