An equiconvex lens having spherical surfaces of radius $10 \mathrm{~cm}$, a central thickness of $2 \mathrm{~cm}$, and a refractive index of $1.61$ is situated between air and water $(n=1.33)$. An object $5 \mathrm{~cm}$ high is placed $60 \mathrm{~cm}$ in front of the lens surface. Find the cardinal points for the lens and the position and size of the image formed.

Show that the lens equation can be written in the Newtonian form $x x^{\prime}=f^{2}$, where x is the distance of the object from the focal point on the front side of the lens, and $x^{\prime}$ is the distance of the image to the focal point on the other side of the lens. Calculate the location of an image if the object is placed 45.0 cm in standard form of the thin lens equation with a focal length f of 32.0 cm.

A racing bicycle has 28 in. diameter tires. The front gears (at the pedals) have 53 teeth and 39 teeth. The largest rear gear has 21 teeth and the smallest has 11 teeth. Determine the maximum speed of the bicycle (to the nearest tenth of a mile per hour) if the cyclist’s cadence is 90 revolutions of the pedals per minute.

Write a function named swapFrontBack that takes as input an array of integers and an integer that specifies how many entries are in the array. The function should swap the first element in the array with the last element in the array. The function should check if the array is empty to prevent errors. Test your function with arrays of different length and with varying front and back numbers.

A converging lens and a diverging lens, separated by a distance of 30.0 cm, are used in combination. The converging lens has a focal length of 15.0 cm. The diverging lens is of unknown focal length. AN object is placed 20.0 cm in front of the converging lens; the final image is virtual and is formed 12.0 before the diverging lens. What is the focal length of the diverging lens?

Suppose a person's nearpoint distance is $67.0 \mathrm{~cm}$. Is the refractive power of the eyeglasses that allow this person to focus on an object just $25.0 \mathrm{~cm}$ from the eye greater than or less than $2.53$ diopters, which is the refractive power when the near-point distance is $57.0 \mathrm{~cm}$ ? The glasses are worn $2.00 \mathrm{~cm}$ in front of the eyes.

A person going for a morning jog on the deck of a cruise ship is running toward the bow (front) of the ship at $2.0 \mathrm{~m} / \mathrm{s}$ while the ship is moving ahead at $8.5 \mathrm{~m} / \mathrm{s}$. What is the velocity of the jogger relative to the water? Later, the jogger is moving toward the stern (rear) of the ship. What is the jogger's velocity relative to the water now?

Consider a program in which data on clients is to be stored in sorted order. The common operations are addition and deletion of clients as well as printing the list of clients from front to back. Which is the most appropriate data structure for storing the client data? (A) An array, (B) A singly linked linked list, (C) A doubly linked linked list, (D) A stack, (E) A queue.

Standing $2.3 \mathrm{~m}$ in front of a small vertical mirror, you see the reflection of your belt buckle, which is $0.72 \mathrm{~m}$ below your eyes. If you now move backward until you are $6.0 \mathrm{~m}$ from the mirror, will you still see the buckle, or will you see a point on your body that is above or below the buckle? Explain.

Sodium light that has a wavelength equal to $589 \mathrm{~nm}$ falls normally on a $2.00$-cm-square diffraction grating ruled with 4000 lines per centimeter. The Fraunhofer diffraction pattem is projected onto a screen a distance of $1.50 \mathrm{~m}$ from the grating by a $1.50$-m-focal-length lens that is placed immediately in front of the grating. Find the resolution in the first order.

Suppose a person's eyeglasses have a focal length of $-301 \mathrm{~cm}$, are $2.00 \mathrm{~cm}$ in front of the eyes, and allow the person to focus on distant objects. Is this person's far point greater than or less than $323 \mathrm{~cm}$, which is the far point for glasses the same distance from the eyes and with a focal length of $-321 \mathrm{~cm}$ ? Explain.

An object is placed 3 cm in front of a concave mirror with a focal length of 6 cm Which set of phrases describes the type of image formed and its magnification? (A) virtual image, twice as large as object (B) virtual image, half as large as object (C) real image, twice as large as object (D) real image, half as large as object

An opera singer in a convertible sings a note at $600\text{ Hz}$ while cruising down the highway at $100\text{ km}/\text{h}$. The speed of sound in the air is $343\text{ m}/\text{s}$.

A) What is the frequency heard by a person standing beside the road in front of the car?

B) What is the frequency heard by a person standing beside the road behind the car?

A person going for a morning jog on the deck of a cruise ship is running toward the bow (front) of the ship at $2.5 \mathrm{~m} / \mathrm{s}$ while the ship is moving ahead at $8.8 \mathrm{~m} / \mathrm{s}$. What is the velocity of the jogger relative to the water? Later, the jogger is moving toward the stern (rear) of the ship. What is the jogger's velocity relative to the water now?