Ch 34: Geometric Optics

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 34: Geometric Optics

Problem 23

Chapter 34, Problem 23

The glass rod of Exercise 34.22 is immersed in oil (n = 1.45). An object placed to the left of the rod on the rod's axis is to be d 1.20 m inside the rod. How far from the left end of the rod must the object be located to form the image?

Verified step by step guidance

Identify the physical situation: A glass rod is immersed in oil, and an object is placed to the left of the rod on its axis. The goal is to find the position of the object such that its image forms 1.20 m inside the rod.

Recall that the image formation inside the rod depends on the refraction of light at the interface between the oil and the glass rod. The key concept here is the apparent depth or the refraction of light between two media with different refractive indices.

Use the relationship between real depth (d), apparent depth (d'), and refractive indices: \(d' = d \times \frac{n_2}{n_1}\), where \(n_1\) is the refractive index of the medium where the object is located (oil, \(n=1.45\)), and \(n_2\) is the refractive index of the rod (glass, which you should find from Exercise 34.22 or assume a typical value).

Set the apparent depth \(d'\) equal to 1.20 m (the image position inside the rod) and solve for the real distance \(d\) from the left end of the rod where the object must be placed.

Express the final formula for the object distance as \(d = d' \times \frac{n_1}{n_2}\), and substitute the known values to find the required object position relative to the left end of the rod.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Refraction

Refraction is the bending of light as it passes from one medium to another with a different refractive index. This phenomenon occurs because light travels at different speeds in different materials. The degree of bending can be described by Snell's Law, which relates the angles of incidence and refraction to the indices of refraction of the two media.

Refractive Index

The refractive index (n) is a dimensionless number that describes how fast light travels in a medium compared to its speed in a vacuum. A higher refractive index indicates that light travels slower in that medium. In this case, the oil has a refractive index of 1.45, which will affect how light behaves as it moves from the glass rod into the oil.

Optical Axis

The optical axis is an imaginary line that defines the path along which light travels through an optical system, such as a lens or a rod. In this scenario, the object is placed along the optical axis of the glass rod, which is crucial for determining the position where the light rays converge or diverge, ultimately affecting the image formation.

Recommended video:

Guided course

13:46

Parallel Axis Theorem

Related Practice

Textbook Question

A person is lying on a diving board 3.00 m above the surface of the water in a swimming pool. She looks at a penny that is on the bottom of the pool directly below her. To her, the penny appears to be a distance of 7.00 m from her. What is the depth of the water at this point?

views

Textbook Question

The left end of a long glass rod 8.00 cm in diameter, with an index of refraction of 1.60, is ground and polished to a convex hemispherical surface with a radius of 4.00 cm. An object in the form of an arrow 1.50 mm tall, at right angles to the axis of the rod, is located on the axis 24.0 cm to the left of the vertex of the convex surface. Find the position and height of the of the arrow formed by paraxial rays incident on the convex surface. Is the erect or inverted?

views

Textbook Question

A converging lens with a focal length of 70.0 cm forms an image of a 3.20 cm tall real object that is to the left of the lens. The image is 4.50 cm tall and inverted. Where are the object and image located in relation to the lens? Is the image real or virtual?

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.

views

Textbook Question

A lens forms an of an object. The object is 16.0 cm from the lens. The is 12.0 cm from the lens on the same side as the object. What is the focal length of the lens? Is the lens converging or diverging?

views

Textbook Question

A Spherical Fish Bowl. A small tropical fish is at the center of a water-filled, spherical fish bowl 28.0 cm in diameter. Find the apparent position and magnification of the fish to an observer outside the bowl. The effect of the thin walls of the bowl may be ignored.

views