Day 6: Diverging
Lenses
P.A. F C F’ C: Optical Center F: Principal Focus F’: Secondary Focus f: focal length PA: Principal Axis f
2F F F’ 2F’ Image Characteristics: In front of object Location: ______Smaller Size: ______Upright Attitude: ______Virtual Type: ______
2F F F’ 2F’
Thin Lens Equation: ______Magnification Equation: ______
Equation Rules:
All distances are measured from the optical center. 1) ______Distances of REAL objects and images are POSITIVE. 2) ______Distances of VIRTUAL objects and images are NEGTIVE. 3) ______Object heights are POSITIVE when ABOVE THE P.A.. 4) ______
Examples:
1. An object 8 cm high is 18 cm from a converging lens having a focal length of 10 cm. a) What are the characteristics of the image? b) How far is the image from the lens? c) How tall is the image? Larger, real, inverted
di = 22.5 cm hi = -10 cm
2. A diverging lens has a focal length of 4 cm. If an object is placed 8 cm from the lens, how far from the lens is the image?
Remember, f is NEGATIVE!!!
di = -2.67 cm
3. Where must a postage stamp be placed in front of a magnifying glass (f = 10 cm), if a virtual image is to be formed 25 cm in front of the lens? Hint: What kind of lens must it be???
Must be a magnifying glass (converging lens)
do = 7.14 cm
4. A lamp 10 cm high is placed 60 cm in front of a diverging lens of focal length 20 cm. Calculate
a) the image position. b) the magnification of the image. di = -15 cm (negative b/c its virtual) c) the height of the image. M = ¼ (must be smaller in diverg. lens)
hi = 2.5 cm (positive b/c its upright)
5. A typical single lens reflex (SLR) camera has a converging lens with focal length 50 mm. What is the position and size of the image of a 25 cm tall candle located 1 m from the lens?
d = 5.26 cm or 52.6 mm (very close to primary focus) i
hi = -1.316 cm (negative b/c its inverted)
6. A converging lens with focal length 20 cm is used to create an image of the sun on a paper screen. How far from the lens must the paper be placed to produce a clear image?
To burn the paper, you must get a REAL image of the sun to form
on the paper. Since the sun is VERY far away, this image will appear VERY close to the primary focus. Therefore, di = 20 cm.
7. The focal length of a slide projector’s converging lens is 10 cm.
a. If a 35 mm slide is positioned 10.2 cm from the lens, how far away must the screen be placed to create a clear image?
b. If the height of a dog on the slide film is 12.5 mm, how tall will the dog’s image on the screen be?
c. If the screen is then removed to a point 15 m from the lens, by how much will the separation between film and lens have to change from part “a”?
di = 510 cm or 5.1m (far away from the film projector)
hi = -62.5 cm (film projectors make the object on the film BIGGER)
New do is 10.07 cm. Old do was 10.2 cm. The difference b/w the two is .13 cm or 1.3 mm.