PHYS 1C Lecture Notes - Lecture 16: Curved Mirror, Thin Lens

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23 May 2018

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Convex mirror

The object in front of the convex mirror

The image is virtual, upright, and smaller than the object (reduced)

Spherical Mirrors

Ray 1: parallel to axis, ray diverted so it or its virtual ray goes

through focal point

Ray 2: directed to focal point, gets reflected parallel to axis

Ray 3: directed to center of curvature, reflected back

Ray Rules

A convex mirror is sometimes referred to a diverging mirror

The rays from any point on the object diverge after reflection as if

they were coming from some point behind the mirror

The image is virtual because it lies behind the mirror at the point

where the reflected rays appear to originate

In general, the image formed by a convex mirror is upright, virtual,

and diminished

Convex Mirrors

What if we wanted to use refraction to converge parallel light rays

to a single focal point? What type of shape should we use?

A parallel light ray was pushed downward

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What happened when we flipped the prism?

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A parallel light ray was pushed upward

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Recall our prism example:

This is the basis behind constructing different types of lenses for

distorting light

This is known as a converging lens

○

It is a lens consisting of plastic or glass that refracts light

○

If focuses parallel light rays at a single point known as the

focal point

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We can construct the following lens:

Converging Lenses

Converging lenses are thick in the middle and thin near the edges

They have positive focal lengths

A thin lens has two focal points, corresponding to parallel light rays from left or from the

right

This is known as a diverging lens

○

It is also a lens consisting of plastic or glass that refracts light

○

It defocuses parallel light rays to make it appear that it came from a single point

We can also construct the following lens

Diverging lenses

(16) Lecture 26B Converging and Diverging lenses

Monday, May 14, 2018

10:58 AM

week 6 Page 1

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Document Summary

The object in front of the convex mirror. The image is virtual, upright, and smaller than the object (reduced) Ray 1: parallel to axis, ray diverted so it or its virtual ray goes through focal point. Ray 2: directed to focal point, gets reflected parallel to axis. Ray 3: directed to center of curvature, reflected back. A convex mirror is sometimes referred to a diverging mirror. The rays from any point on the object diverge after reflection as if they were coming from some point behind the mirror. The image is virtual because it lies behind the mirror at the point where the reflected rays appear to originate. In general, the image formed by a convex mirror is upright, virtual, and diminished. This is the basis behind constructing different types of lenses for distorting light. It is a lens consisting of plastic or glass that refracts light.

Related Questions

An object O is placed at the location shown in front of a concavespherical mirror. Use ray tracing to determine the location andsize of the reflected image. As you work, keep in mind thefollowing properties of principal rays:

A ray parallel to the axis, after reflection, passes through thefocal point F of a concave mirror or appears to come from the(virtual) focal point of a convex mirror.
A ray through (or proceeding toward) the focal point F is reflectedparallel to the axis.
A ray along the radius through or away from the center of curvatureC intersects the surface normally and is reflected back along itsoriginal path.
A ray to the vertex V is reflected, forming equal angles with theoptic axis.

a candle is placed in front of a convex mirror.

A candle is placed in front of a convex mirror.

Figure6 of 6The figure labeled C shows two rays coming out of the top of the object in front of the concave mirror, forming an acute angle with the axis. Upper ray reflects parallel to the axis. And the lower ray reflects in the direction exactly opposite to its initial direction. There is a focus point F on the axis in front of the mirror and a center of the mirror’s curvature C between point F and the object. The image is smaller, than the object, located between points F and C, and inverted, its tip is formed by intersection of the reflected rays. The initial upper ray passes through point F and the initial upper ray passes through point C. The figure labeled C shows two rays coming out of the top of the object in front of the concave mirror, forming an acute angle with the axis. Upper ray reflects parallel to the axis. And the lower ray reflects in the direction exactly opposite to its initial direction. There is a focus point F on the axis in front of the mirror and a center of the mirror’s curvature C between point F and the object. The image is smaller, than the object, located between points F and C, and inverted, its tip is formed by intersection of the reflected rays. The initial upper ray passes through point F and the initial upper ray passes through point C.

Part A Consider the following diagrams noting that the scale is different between diagrams. In these diagrams, C and F represent the center of curvature and the focal point of the convex mirror, respectively. The image formed by the mirror is obtained using the ray tracing technique. Which diagram(s) are correct?(Figure 1) (Figure 2) (Figure 3) Type A if you think that only diagram A is correct, type AB if you think that only diagrams A and B are correct, and so on.

Part B If the radius of curvature of the convex mirror is 50.0 cm , at what distance do from the mirror must the candle be placed so that its image is formed 20 cm from the mirror? Express your answer in centimeters. View Available Hint(s) dod o d_o = cm The convex mirror is now replaced by a concave mirror with the same radius of curvature.

Part C Consider the following diagrams, where now C and F represent, respectively, the center of curvature and the focal point of the concave mirror. Again, the image formed by the mirror is found by ray tracing. Choose the correct diagram(s).(Figure 4) (Figure 5) (Figure 6) Type A if you think that only diagram A is correct, type AB if you think that only diagrams A and B are correct, and so on. View Available Hint(s)

Part D Assuming that the candle remains at a distance do from the mirror (the same distance found in Part B), at what distance di from the mirror will its image form now? Express your answer in centimeters. View Available Hint(s) did i d_i = nothing cm

jadeelk940

If a virtual image is formed 9.0 cm along the principal axis from aconvex mirror of focal length â15.0 cm, how far is the object fromthe mirror?

2. A woman looking in a makeup mirror sees her face at twice itsactual size and right-side up. If she is 26.0 cm from the mirror,what is its focal length?

3. Which of the following best describes the image of a concavemirror when the object is at a distance greater than twice thefocal point distance from the mirror?
a. virtual, upright and magnification greater than one
b. real, inverted and magnification less than one
c. virtual, upright and magnification less than one
d. real, inverted and magnification greater than one

4. A convex mirror with focal length of ?18 cm forms an image 12 cmbehind the surface. Where is the object located as measured fromthe surface?

5. A convex mirror with a focal length of ?18 cm forms an image 15cm behind the surface. If the object height is 1.2 cm what is theimage height?

6. An object placed 14 cm from a concave mirror produces a realimage 8.0 cm from the mirror. If the object is now moved to a newposition 18.0 cm from the mirror, where is the new image located asmeasured from the mirror?

7. When the reflection of an object is seen in a concave mirror theimage will:

8. A candle is 40.0 cm in front of a convex spherical mirror ofradius of curvature 70.0 cm. What are the image distance and themagnification, respectively?

9. An object is 16.0 cm from the surface of a spherical Christmastree ornament that is 8.00 cm in diameter. What is themagnification of the image?

10. A solid glass sphere with a radius of 6.00 cm and index ofrefraction of 1.50 has a small coin embedded 3.00 cm from the frontsurface of the sphere. For the viewer looking at the coin throughthe glass, at what distance from the front surface of the glassdoes the coinâs image appear to be located?

11. A glass block, for which n = 1.52, has a blemish located 4.5 cmfrom one surface. At what distance from that surface does the imageof the blemish appear to the outside observer?

12. An object of length 2.00 cm is inside a plastic block withindex of refraction 1.50. If the object is viewed from directlyabove, what is the length of its image?

13. An object is placed at a distance of 25 cm from a thin convexlens along its axis. The lens has a focal length of 10 cm. What arethe values, respectively, of the image distance andmagnification?
14. An object is placed at a distance of 50 cm from a thin lensalong the axis. If a real image forms at a distance of 35 cm fromthe lens, on the opposite side from the object, what is the focallength of the lens?

15. A contact lens is made of plastic with an index of refraction1.50. The lens has an outer radius of curvature of +2.0 cm and aninner radius of curvature of +2.5 cm. What is its focallength?

16. A Youngâs double slit has a slit separation of 2.50 ? 10?5 m onwhich a monochromatic light beam is directed. The resultant brightfringes on a screen 2.00 m from the double slit are separated by2.30 ? 10?2 m. What is the wavelength of this beam? (1 nm = 10?9m)

17. A Youngâs double-slit apparatus is set up so that a screen ispositioned 1.9 m from the double slits, and the spacing between thetwo slits is 0.040 mm. What is the distance between alternatingbright fringes on the screen if the light source has a wavelengthof 630 nm? (1 nm = 10?9 m)

18. The blue tint of a coated camera lens is largely caused by whateffects?

19. What is the minimum thickness of a glycerin film (n = 1.47) onwhich light of wavelength 650 nm shines that results inconstructive interference of the reflected light? Assume the filmis surrounded front and back by air.

20. Light of wavelength 560 nm is incident on a slit of width 0.150mm, and a diffraction pattern is produced on a screen that is 2.00m from the slit. What is the width of the central bright fringe? (1nm = 10?9 m)

21. Light of wavelength 610 nm is incident on a slit of width 0.25mm, and a diffraction pattern is produced on a screen that is 1.5 mfrom the slit. What is the distance of the second dark fringe fromthe center of the bright fringe? (1 nm = 10?9 m)

22. A multiple slit diffraction grating has a slit separation of2.50 ? 10?6 m. Find the wavelength of the monochromatic light thatwill have its second order bright fringe diffracted through anangle of 38.0Â°. (1 nm = 10?9 m)

23. A diffraction grating with 12 000 lines/cm will exhibit thefirst order maximum for light of wavelength 510 nm at what angle?(1 nm = 10?9 m)

24. A beam of unpolarized light in air strikes a flat piece ofglass at an angle of incidence of 58.0Â°. If the reflected beam iscompletely polarized, what is the index of refraction of theglass?

25. A beam of polarized light of intensity I0 passes through asheet of ideal polarizing material. The polarization axis of thebeam and the transmission axis of the sheet differ by 45Â°. What isthe intensity of the emerging light?

26. At what angle is the sun above the horizon if its light isfound to be completely polarized when it is reflected from the topsurface of a slab of glass (n = 1.65)?

PHYS 1C Lecture Notes - Lecture 16: Curved Mirror, Thin Lens

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