LECTURE 12SPHERICAL MIRRORS

Instructor: Kazumi Tolich

Lecture 12

¨ Reading chapter 26.3 to 26.4¤ Concave and convex spherical mirrors¤ Ray tracing¤ Mirror equation & magnification

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Spherical mirrors’ focal points and lengths

¨ Parallel rays hitting a spherical mirror come together at the focal point for a concave mirror.

¨ They appear to have come from the focal point for a convex mirror.¨ The focal length, 𝑓, in terms of the radius of the curvature, 𝑅, is

𝑓 = ± %&𝑅 (+ for concave, − for convex mirrors)

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Spherical aberration

¨ Spherical aberration, blurring of the image, can be remedied by using only rays near the principal axis (paraxial rays) or a parabolic mirror instead.

¨ In our study of spherical mirrors, we assume we only use paraxial rays.

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Quiz: 1

¨ When the distance between the mirror and the object is much larger than the radius of the curvature of the mirror, how far away from the mirror is the image formed in terms of the focal length, 𝑓? Enter the number without 𝑓.

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Quiz: 12-1 answer/Demo: 1

¨ 1

¨ Since the object is very far away from the mirror, the rays from that object is parallel to each other.

¨ If an object is placed at a focal point, the rays emerge parallel to each other.

¨ One Candle Searchlight¤ Demonstration of object placed at the focal plane of the mirror.

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Ray tracing

¨ The ray tracing yields the orientation, location, and size of the image.¨ The image produced by a spherical mirror is located at the cross point of three

principal rays.¤ The parallel ray (P ray) reflects through the focal point.¤ The focal ray (F ray) reflects parallel to the axis. ¤ The center-of-curvature ray (C ray) reflects back along its incoming path.

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Quiz: 2

¨ Ray tracing is shown in the figure. Which of the following statements is/are correct? Choose all that apply.A. The image is a virtual image.B. The image is a real image.

C. The image is upright.D. The image is magnified.

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Quiz: 12-2 answer

¨ The image is a virtual image.

¨ The image is upright.¨ An image is called a virtual image if light does not really come from the image point. A virtual

image cannot be projected.¨ An image is called a real image if light really comes from the image point. An real image can

be projected.

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Mirror equation

¨ The mirror equation gives the relationship among the focal length 𝑓, the object distance 𝑑*, and the image distance 𝑑+.

1𝑑*+1𝑑+=1𝑓

¨ The magnification, 𝑚, is defined to be

𝑚 ≡ℎ+ℎ*= −

𝑑+𝑑*

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Sign conventions

¨ Focal length, 𝑓:¤ + for concave mirrors

¤ − for convex mirrors

¨ Magnification, 𝑚:¤ + for upright image¤ − for inverted image

¨ Image distance, 𝑑+:¤ + for images in front of a mirror (real images)¤ − for images behind a mirror (virtual images)

¨ Object distance, 𝑑*:¤ + for objects in front of a mirror (real objects)

¤ − for objects behind a mirror (virtual objects)

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Quiz: 3

¨ When you place your face near a spherical concave mirror, inside its focal point, which of the following is/are correct? Choose all that apply. The image of your face isA. Diminished.B. Enlarged.C. Upright.D. Inverted.E. Real.F. Virtual.

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Quiz: 12-3 answer

¨ Enlarged, Upright, Virtual.¨ This is how make-up/ shaving mirror works.

¨%01+ %

02= %

3, where 0 < 𝑑* < 𝑓. 𝑑+ =

0130163

< 0, so the image is virtual.

¨ 𝑚 = − 0201> 0, so the image is upright.

¨ 𝑚 = 0201

=81981:9

01= 3

3601> 1, so the image is enlarged.

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Your face here. Your face image here.

Quiz: 4

¨ An object is placed between the center of curvature and the focal length of a concave mirror. Which of the following is/are correct about the image formed? Choose all that apply.

A. RealB. VirtualC. UprightD. InvertedE. EnlargedF. Diminished

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Quiz: 12-4 answer/Demo: 2

¨ Real, inverted, and enlarged

¨%01+ %

02= %

3, where 𝑓 < 𝑑* < 2𝑓 = 𝑟. 𝑑+ =

0130163

> 0, so the image is real.

¨ 𝑚 = − 0201< 0, so the image is inverted.

¨ 𝑚 = 33601

> 1, so the image is enlarged.

¨ Large Concave Mirror with Strawberries and Candles¤ Demonstration of object placed outside of the focal point, forming a real inverted image.

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Quiz: 5

¨ A convex mirror has a radius of curvature of 24 cm. What is the image distance for an object located near the axis at distance of 12 cm from the mirror in cm?

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Quiz: 12-5 answer

¨ −6  cm  

¨ 𝑅 = 24  cm, so 𝑓 = − %&𝑅 = −12  cm.

¨%01+ %

02= %

3

¨ 𝑑+ =0130163

= %&  BC 6%&  BC%&  BC 6 6%&  BC

= −6  cm

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Quiz: 6

¨ A convex mirror has a radius of curvature of 24 cm. An object is located near the axis at distance of 12 cm from the mirror. Which of the following descriptions is correct about the image formed? Choose all that apply.A. RealB. VirtualC. UprightD. InvertedE. EnlargedF. Diminished

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Quiz: 12-6 answer

¨ It’s always virtual, upright, and diminished.¨ 𝑑* = 12  cm¨ 𝑓 = −12  cm¨ 𝑑+ = −6  cm¨ 𝑑+ = −6  cm < 0, so the image is virtual.

¨ 𝑚 = − 0201= − 6D  BC

%&  BC> 0, so the image is upright.

¨ 𝑚 = − 6D  BC%&  BC

= 0.5 < 1, so the image is diminished.

¨ All images of a convex mirror are always virtual, upright, and diminished.

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