3 easy to trace lines can help locate the image formed by a lens

With the magnification,

ConcepTestConcepTest

air

water

If a glass lens in air focuses a light as shown, which of the figures best illustrates how the light will focus in water?

p q

For a given lens (of fixed focal length, f ), as the object approaches the focal point( p f ), the image position, q, approaches

(1) 0.(2) f / 2.(3) f.(4) 2f.(5)

p q

For a given lens (of fixed focal length, f ), asthe object moves very far back from the lens( p ), the image position, q, approaches

(1) 0.(2) f / 2.(3) f.(4) 2f.(5)

Some Answers to Concept Questionsnair 1.0 nwater = 1.3 nglass=1.5With water surrounding the glass lens, the transition acrossboundaries involves a much smaller change in density,a smaller shift in light speed. If the speed of light changesless, the resulting change in direction will be less pronounced.

(5) For this fixed height object, the yellow line will still enter the lens at the same height as the object is moved closer, following the same path oncethrough the lens. Notice how the red line, pinned to the objects tip on oneend, and through the focus, rotates as the object moves in closer. It turnsdownward intercepting the lens at a progressively lower point…that meansthe refracted red line meets the yellow line closer and closer to the axis…and closer and closer to the focus. The white line, pivoting about the pointAt the lens’ center exhibits the same behavior.

(3) f. Following a argument similar to above: see how the light raystraced will shift. OR look at the thin lens equation: 1/f = 1/p + 1/q.With f (and thus the left-hand-side of the equation) fixed, as p ,1/p 0. So 1/f 1/q.

MORE

A light source is held near a lens and its light focuses at point B, as shown in the top figure. If the light source is moved closer to the lens, then at which of the indicated points will the light focus?

(1) A(2) B(3) C

In the figure at top, a simple single lens camera is focused on a distant mountain.

The camera is then focused on a nearby person.

Which of the figures at left best illustrates the lens position to focus on the person?

A light source is held near a lens and its light focuses at point B, as shown in the top figure. If the light source is moved closer to the lens, then at which of the indicated points will the light focus?

Conceptually: Bending power of the lens is the same in both cases. For a closer object, the rays diverge more, and so it takes longer for them to be brought to a convergence.Mathematically: 1/i + 1/o = 1/f If o gets shorter (1/o bigger), then i must get longer (1/i smaller) since f does not change.

In the figure at top, a simple single lens camera is focused on a distant mountain.

The camera is then focused on a nearby person. Which of the figures at left best illustrates the lens position to focus on the person?

o becomes smaller (1/o bigger), so i must become bigger (1/i smaller) so that 1/f = 1/i + 1/o

film

A magnifying glass has f =30 cm. If the object to be viewed is at p = 10 cm. Locate the image. What kind of image is formed? What is the magnification factor?

q

1

cm 10

1

cm 30

1

If p=150 cm where will the image form? Magnification? Kind of image?

cm 30

21 q

cm 15q

5.1 cm) cm/10 15( Mvirtual image!

q

1

cm 150

1

cm 30

1 cm 5.37q

25.0 cm/150cm)5.37( M

p dobj object’s distance to lens or mirroralways positive (for real objects)

f=R/2 for spherical approximations to parabolas

focal length POSITIVE for CONVERGINGNEGATIVE for DIVERGING

q dimage distance image comes into focus from lens or mirror

POSITIVE means REAL IMAGENEGATIVE means VIRTUAL IMAGE

M -q/p = -dimage/dobjMAGNIFICATION: