Thin Lens And Lens Maker Equations Practice Problems

A physics student enhanced a classical microscope by replacing the traditional eyepiece with an ocular camera, enabling direct imaging of microscopic samples. The camera's sensor has a width of 25 mm and individual pixels measure 3.5 μm × 3.5 μm. If a microorganism structure appears with a length of 100 pixels in the captured image, what is the actual length of the microorganism structure in μm? Consider the magnification of the microscope as 100.

A pair of lenses is used to focus an object on a wall. The object is 1.50 m away from the wall, 15.0 cm to the left of a -18.0 cm lens. The second lens with focal length f is placed at a distance d to the right of the first lens. Given that the magnification due to the second lens is -7.33, calculate f and d.

An optical engineer is designing an achromatic lens for a new microscope. The engineer combines two lenses of different materials and shapes (plano-concave and bi-convex), as shown in the image below. As a result, all the wavelengths of light will focus at the same distance, resulting in a sharper image. The engineer starts by selecting two materials for her lenses. The plano-concave lens has refractive indices n _1,b and n _1,r for blue and red wavelengths, respectively. The bi-convex lens has refractive indices n_2,b, and n_2,r for blue and red wavelengths, respectively. The curved side of the plano-concave lens and the curved side of the bi-convex lens have an equal radius of curvature, R. Determine the relation between n _2,b - n_2,r, and n_1,b -n_1,r in order that the different wavelengths focus on the same point and eliminate chromatic aberration.

In an advanced infrared laser system, a plano-concave lens composed of germanium is used. The lens, with its flat side facing the object, produces an image from an infrared source. The magnification of this produced image is +0.40, and the distance from the infrared source to the lens is 50 cm. Given that the refractive index of germanium is 4.01, calculate what the radius of curvature will be for the curved surface of the lens.

A laboratory technician is observing a specimen on a slide using a symmetric (biconvex) lens made from glass. The slide is positioned 40 cm from the viewing screen. What should be the radius of the lens in order to produce an image of the specimen on the viewing screen that appears to be three times bigger than the actual size of the specimen?

A sports photographer uses a camera with a 300 mm focal-length lens to capture a track athlete. The athlete is initially at a distance of 50 m from the photographer before they begin running directly towards the photographer at a speed of 10.0 m/s. Determine the velocity of the image of the athlete as seen through the camera lens in μm/s. Also, determine whether the image is moving closer to or further away from the lens.

Consider a plano-convex lens that is flat on one side, has a 15.0 cm radius of curvature on the other lens, and is composed of magneto-optical plastic. This plastic has an index of refraction of 1.550. The lens is being used to form an image of an object situated 60.0 cm from the lens on a viewing screen. If a magnetic field is applied to the plastic, causing the index of refraction to decrease, what change in the refractive index would be necessary to shift the image 4.0 cm further away from the lens?

A jeweller has crafted a symmetric converging diamond lens with a refractive index of 2.42. The lens has two equally curved surfaces with a radius of 1.0 cm. Calculate its focal length in both air and ethanol. The refractive index of ethanol is 1.36.

An optometrist using a plano-convex lens made from polycarbonate that has a radius of curvature of 15 cm. A 1.0 cm tall letter is found on a vision test chart that is placed 18 cm away and is facing in front of a lens. Determine the (i) position and (ii) height of the image formed by the lens.

A photographer is taking a photograph of a person who is standing 3.0 m away from her. She is using a camera with a 50 mm focal length lens. The person's face is approximately 20 cm long in height. What is (i) the image distance and (ii) the height of the person's face image on the camera's sensor?

A lepidopterist uses a magnifying glass (a type of converging lens) that has a focal length of 10.0 cm to inspect a moth that is 2.0 cm long. The moth is placed 9.0 cm away from the lens. Calculate the numerical values for: (i) the position s' and (ii) the height h' of the image.

A child is playing with a large, perfectly spherical sapphire marble that has a refractive index of n = 1.77 and a diameter of 8.0 cm. She places a small figurine 4.8 cm away from the edge of the marble and notices that an image of the figurine forms on the opposite side of the marble. Consider what would happen if the marble was replaced with a thin lens that is placed where the center of the marble had been located originally and if the image remains in the same position, what would be the lens's focal length in this case?

An engineer is working on an optical communications system and wants to focus a light beam from a semiconductor laser diode (that has a wavelength of λ = 1310 nm) to a specific spot that has a diameter of 50 μm on a photodiode which is located 5.0 cm behind a lens. Determine what has to be the minimum diameter value for this particular lens.

We use concentrated laser light in laser spectroscopy to make atoms or molecules do something special — called 'excitation'. This special state can help us understand more about these atoms or molecules. Imagine you're creating a setup for this kind of experiment. You're using a red laser that emits light with a wavelength of 633 nm. In your setup, what you want to study is placed at the focus 1.0 m away from the lens. Your calculations tell you that the laser light must be narrowed down to a 0.5 mm in diameter spot. With this in mind, what is the smallest diameter your lens can be to achieve this?

A biconcave lens is made from fused quartz (refractive index 1.46) is shown below. Compute the focal length of this lens.

In an optical setup, two lenses with a separation of 8.00 cm are used. The first is a converging lens with a focal length of 15.0 cm placed to the left of a diverging lens with a focal length of -30.0 cm. i) Determine the effective focal length of the lens combination. ii) Determine the position of the principal plane measured with respect to the diverging lens.

A toy projector is placed on a nightstand and projects an image onto the ceiling of a room. The produced image is 6 times bigger than the original 4.0-cm-tall object. The object is 2.45 m from the ceiling. Determine the projector's focal length.

A science instructor holds her phone 2.0 m away from a whiteboard. The teacher wants to magnify the device's screen three times using a lens. Determine the focal length and distance at which the lens should be positioned (with respect to the phone) to obtain this effect.

A student uses a converging lens with a focal length of 5.0 cm to produce a real image of a bug by varying the position of the lens. Find the shortest possible distance between the bug and its image.

A Xerox machine uses a thin lens to make an image of a document on its drum. This image is then used to make the copy. A passport is put on the xerox machine's document glass, which is 20 cm from the lens. The image formed is 15.0 cm from the lens and is on the opposite side. Determine the focal length and find out whether the lens is converging or diverging.

A plano-convex lens forms an image of an action figure 12.4 cm tall and is placed to its left. The image of the action figure is inverted and has a height of 16.2 cm. The lens is flat on one side and has a focal length of 85cm. Determine the image and object positions with respect to the lens. Should the image be real or virtual?

A highly polished, double convex lens with a 130 mm focal length and 44 mm diameter forms an image of an object placed in front of it. The image formed by the convex lens is 2.1 cm tall and erect. The height of the object is 15 mm. Find out how far from the lens is the image and object located. Is the image erect or inverted?

Emily suffers from farsightedness. She went to an optical consultant to help her choose the perfect frame with the highest quality lens for her glasses. The glass she opted for has an index of refraction of n = 1.45 and a focal length of 15 cm. Determine the radius when both surfaces of the lens have the same radii.

The are two types of thin lens, (converging and diverging) the most basic are depicted in the figure below. For each lens shown find how far from the lens the image of an object is, which is placed 22cm to the left of the lens. The index of refraction of the lens material is 1.43.

A 1-cm-height fly is placed 10 cm to the left of a lens. On the other side of the lens, the image of the fly is observed 15 cm from the lens. i) Determine the height of the observed image. ii) Is the image inverted or non-inverted relative to the fly?

A science teacher desires to use a lens to project the screen of her smartphone onto a whiteboard 3.00 m away from the phone. The phone is placed 30.0 cm to the left of the lens. The screen of the smartphone has a width of 5.00 cm and a length of 10.0 cm. Determine the minimum dimensions of the whiteboard necessary to fit the image dimensions.

A student builds an optical system by placing coaxially two lenses (L₁) and (L₂) 5 cm apart. (L1) is a divergent lens of focal length f₁ = -10 cm, while (L₂) is a convergent lens of focal length f₂ = 10 cm. He placed a matchstick at a distance of 8 cm to the left of L₁. i) Determine the location of s'₁, the image produced by L₁. ii) The image produced by L₁ is the object for L₂. Determine the distance s₂ that separates the object from L₂. iii) Find the location of the final image of the two lenses of the optical system.

Determine the f-number of a photographic system having an aperture diameter of 10.5 cm and a focal length of 85.0 cm.

Your science teacher wears a 3.25-diopter contact lens. Determine your teacher's near point.

You have a blurry close-up vision. An eye specialist measures your near point to be 50.0 cm. He tells you that you should wear eyeglasses. If the distance between your eyeball and the glasses is 1.50 cm. i) Determine the focal length of the required eyeglasses to adjust your vision. ii) Express your answer in diopters.

A supermarket cashier has difficulty seeing the prices written on a whiteboard placed at a distance of 1.5 m from him. He prefers to use glasses to rectify his vision. Name the ocular refractive errors causing this vision trouble.

An optometrist prescribes a contact lens to adjust the vision of a student who encounters problems focusing on objects placed above 1.0 m. Determine i) the focal length of the contact lens and ii) its power in diopters.

You are inspecting a jewel with a magnifier. The magnifier is built using a thin lens with a focal length of 4.0 cm. If the jewel is placed at the focal length of the lens, determine the angular magnification of the magnifier. Assume that your nearest point is 28 cm.

You have the ability to see the distance object clearly while the minimum distance on which your eye can focus is 35 cm instead of 25 cm for a normal eye. Identify the ocular refractive errors causing your vision trouble.

A watchmaker's loupe of focal length 4.50 cm is used to magnify the minute wheel of a watch placed 3.85 cm in front of the magnifier. The minute wheel is 2.0 mm tall. Determine the height of the image formed by the loupe.

In a science project, a student built a microscope using two converging lenses. The first lens, forming the microscope's objective, has a focal length of 1.5 cm. The second lens, forming the microscope ocular, has a focal length of 4.5 cm. The first lens forms a real image exactly at the focal length of the ocular. The two lenses are 8.5 cm apart. Determine the strength of the linear magnification produced by the first lens.

A microscope is composed of two optical components. A converging lens (L₁) of focal length 0.7 cm forms an image 15.0 cm to the right of the second focal point of L₁. The image formed by L₁ is very close to the focal point of the second converging lens, L₂. The focal length of L₂ is 2.3 cm. Calculate the total angular magnification of this microscope.

A refracting telescope used for touristic purposes consists of an objective and an eyepiece. The objective is a convergent lens of focal length 1.10 m, and the eyepiece is a convergent lens of focal length 0.18 m. If an object is placed very far from the telescope, the virtual image produced is at infinity. A tourist looks through the telescope to discover the Statue of Liberty. The statue stands 93 meters tall and is located 5.0 kilometers from the telescope. Calculate the height of the image produced by the objective.

In a physics lab experiment on optics, a student uses a converging lens with a focal length of 15 cm to produce an image that exactly matches the size of a thin stick. The stick is placed horizontally along the principal axis of the lens and has a size of 8.0 cm. Determine the distance between the lens and the stick's farthest end.

What is the diameter of the lens aperture necessary to achieve proper exposure when a camera's close-up lens is directed towards a portrait located 150 mm in front of the lens, resulting in a focused image on the detector situated 40 mm behind the lens? The required f-number for this exposure is F5.6.

The Huygens eyepiece follows the principle of minimizing spherical aberration by arranging two plano-convex lenses with their curved surfaces facing each other. An analysis reveals that chromatic aberration is minimised for the Huygens eyepiece when the spacing between the lenses, denoted as L, equals half the sum of their focal lengths L = 1/2(f₁ + f₂). Let's shift our focus to the design of a Huygens eyepiece, aiming to achieve a 12x magnification. Given that the first lens of the Smithson eyepiece has a focal length of 35 mm, calculate the following:

(i) The focal length of the second lens in the Huygens eyepiece.

(ii) The spacing between the first and second lenses in the Huygens eyepiece.