AP Physics 2: 6.5 Images from Lenses and Mirrors – Exam Style questions with Answer- MCQ

Question

A lens and a mirror both have a focal length of f in air. Both are submerged in water, and the focal length \(f_{water}\) is measured for both. How does the focal length under water compare to the focal length in air?

▶️Answer/Explanation

Ans:C

The law of reflection is not influenced by the water. Snell’s law of refraction depends on the indices of refraction of the two materials. The speed of light changes less going from water to lens then going from air to lens. This means there will be less refraction in water, making the focal length larger.

Question

An optics bench is set up on a meter stick, as shown in the figure. The light source is a candle placed at \(x_{0}\). The lens is located at \(x_{1}\). The screen is moved until a sharp image appears at location \(x_{2}\). The data is recorded in a table, the lens is moved to a new location (\(x_{1}\)), and the screen is adjusted until the image is sharp again. Which of the following procedures will allow a student to determine the focal length of the lens?
(A) Plot \(x_{2}\) as a function of \(x_{0}\). The focal length will be the vertical axis intercept.
(B) Plot \((x_{2}-x_{1})\) as a function of \((x_{0}-x_{1})\). The focal length will be the vertical axis intercept.
(C) Plot l/\(x_{2}\) as a function of l/\(x_{0}\). The focal length will be the inverse of the vertical axis intercept.
(D) Plot l/\((x_{2}-x_{1})\) as a function of l/\((x_{0}-x_{1})\). The focal length will be the inverse of the vertical axis intercept.

▶️Answer/Explanation

Ans:D

The lens equation can be rearranged to produce a straight line:

\(\frac{1}{s_{i}}=(-1)\frac{1}{s_{o}}+\frac{1}{f}\)

\(y=mx+b\)

Thus, if we plot 1/\(s_{o}\) on the x-axis and 1/\(s_{i}\) on the y-axis, we should get a graph with a slope of -1 and an intercept of 1/f. The image distance is \(x_{2}-x_{1}\), and the object distance is \(x_{0}-x_{1}\).

Question

 A laser beam passes through a prism and produces a bright dot of light a distance of x from the prism, as shown in the figure. Which of the following correctly explains the change in distance x as the angle \((\theta)\) of the prism is decreased?
(A) The distance x increases because the angle on incidence increases.
(B) The distance x increases because the angle of incidence decreases.
(C) The distance x decreases because the angle on incidence increases.
(D) The distance x decreases because the angle of incidence decreases.

▶️Answer/Explanation

Ans:B

When the angle of the prism decreases, the right side of the prism becomes more vertical, and the angle of incidence with the normal becomes smaller. This creates less refraction and the distance (x) increases. Look at the extreme case when \(\theta\) becomes zero. Then the angle of incidence is zero, and there is no refraction at all. The beam will pass straight through the “prism” because it has become flat like a window, and the distance (x) becomes infinite.

Question

A glass lens of focal length f = 80 cm in air is submerged in oil. How will submerging the lens in oil affect the focal length of the lens and why?
(A) f > 80 cm because there is now a smaller change in velocity as light passes from oil into the glass.
(B) f = 80 cm because the index of refraction of glass has remained unchanged by placing the lens into the oil.
(C) f = 80 cm because the shape of the lens has remained unchanged by placing the lens into the oil.
(D) f < 80 cm because light travels slower in oil.

▶️Answer/Explanation

Ans:

A—When submerged in water, the light will not refract as much passing through the lens, because the speed of the light will not change as much traveling from oil to glass as it did traveling from air to glass. This will move the focal point farther from the lens. In fact, if the oil has the same index of refraction as the glass, light will not change direction as it passed through the lens, because it did not change speed passing through the lens.

Question

A lens is placed between a doll and a white sheet of paper in such a way as to produce an image on the paper. On the side of the lens facing the doll, a dark card is slowly lowered to cover the lens as shown in the figure. Which of the following correctly explains what will happen to the image of the doll?
(A) As the descending card blocks more and more of the lens, the focal point of the lens shifts. This causes the image to become increasingly blurry until the image disappears from the screen.
(B) The image remains clear, but the head of the doll in the image disappears first, followed by the feet, as the light from the top of the object is blocked before the light from the feet.
(C) The image remains clear, but since the doll projects an inverted real image on the screen, the doll’s feet will disappear from view first, followed by the head last, as light from the object is blocked.
(D) As the card blocks light from the object, the image remains clear but becomes increasingly dim until the image disappears.

▶️Answer/Explanation

Ans:

D—Blocking part of the lens does not keep other parts of the lens from producing an image. It just makes the image dimmer because less of the lens is being used to produce the image. This is what happens when you squint to block a bright light. You can still see everything clearly. You just make the image dimmer.

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