Textbook Question
A concave mirror has a radius of curvature of 34.0 cm. If the mirror is immersed in water (refractive index 1.33), what is its focal length?
1
views
Ch 34: Geometric Optics
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
Not the one you use?Change textbookSelect a different textbook
Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 33, Problem 10a
You hold a spherical salad bowl 60 cm in front of your face with the bottom of the bowl facing you. The bowl is made of polished metal with a 35-cm radius of curvature. Where is the of your 5.0-cm tall nose located?
Verified step by step guidance1
Identify the type of mirror: The problem describes a spherical bowl made of polished metal, which acts as a concave mirror. The radius of curvature (R) is given as 35 cm.
Use the mirror equation to find the image distance (\(d_i\)): \(\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}\), where \(f\) is the focal length and \(d_o\) is the object distance. The focal length \(f\) is half the radius of curvature, so \(f = \frac{R}{2} = \frac{35}{2} = 17.5\) cm.
Substitute the known values into the mirror equation: The object distance \(d_o\) is 60 cm (the distance from your face to the bowl). Substitute \(f = 17.5\) cm and \(d_o = 60\) cm into the equation: \(\frac{1}{17.5} = \frac{1}{60} + \frac{1}{d_i}\).
Solve for the image distance \(d_i\): Rearrange the equation to solve for \(\frac{1}{d_i}\): \(\frac{1}{d_i} = \frac{1}{17.5} - \frac{1}{60}\). Calculate \(\frac{1}{d_i}\) and then take the reciprocal to find \(d_i\).
Interpret the result: The sign of \(d_i\) will indicate the nature of the image. A positive \(d_i\) means the image is real and located on the same side as the object, while a negative \(d_i\) indicates a virtual image located on the opposite side of the mirror.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
5mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Mirror Equation
The mirror equation relates the object distance (d_o), image distance (d_i), and the focal length (f) of a spherical mirror: 1/f = 1/d_o + 1/d_i. For a concave mirror, the focal length is half the radius of curvature. This equation helps determine the position of the image formed by the mirror.
Recommended video:
09:03
Mirror Equation
Radius of Curvature
The radius of curvature is the distance from the mirror's surface to its center of curvature. For spherical mirrors, it is twice the focal length. In this problem, the radius of curvature is given as 35 cm, which is crucial for calculating the focal length and subsequently the image position.
Recommended video:
Guided course
06:18Calculating Radius of Nitrogen
Image Formation by Concave Mirrors
Concave mirrors can form real or virtual images depending on the object's position relative to the focal point. If the object is outside the focal length, a real, inverted image is formed. Understanding this concept helps predict the nature and position of the image of the nose in the bowl.
Recommended video:
12:04Ray Diagrams for Concave Mirrors
Related Practice
Textbook Question
An object 0.600 cm tall is placed 16.5 cm to the left of the vertex of a concave spherical mirror having a radius of curvature of 22.0 cm. Determine the position, size, orientation, and nature (real or virtual) of the image.
2
views
Textbook Question
Dental Mirror. A dentist uses a curved mirror to view teeth on the upper side of the mouth. Suppose she wants an erect with a magnification of 2.00 when the mirror is 1.25 cm from a tooth. (Treat this problem as though the object and lie along a straight line.) What must be the focal length and radius of curvature of this mirror?
1
views
Textbook Question
An object is 18.0 cm from the center of a spherical silvered-glass Christmas tree ornament 6.00 cm in diameter. What are the position and magnification of its ?
1
views
Textbook Question
The thin glass shell shown in Fig. E34.15 has a spherical shape with a radius of curvature of 12.0 cm, and both of its surfaces can act as mirrors. A seed 3.30 mm high is placed 15.0 cm from the center of the mirror along the optic axis, as shown in the figure. Calculate the location and height of the of this seed.
1
views
Textbook Question
A spherical, concave shaving mirror has a radius of curvature of 32.0 cm. Where is the image? Is the image real or virtual?
1
views