Question 1

What is the focal length of the corrective contact lens needed by a nearsighted person whose far point is 60 cm?

Accepted Answer

The focal length of the corrective lens for a nearsighted person should allow them to see distant objects clearly. Since their far point is 60 cm, the lens needs to correct vision to infinity. The formula for lens power (P) in diopters is P = 1/f (in meters), where f is the focal length. To make distant objects (at infinity) appear at the person's far point (60 cm or 0.6 meters), the lens must have a focal length of -0.6 meters or -60 cm. Negative because it's a diverging lens, suitable for nearsightedness correction.

Question 2

A camera lens has a focal length of 50.0 mm and an aperture setting of 4.00. What is the aperture diameter of this lens?

Accepted Answer

The answer of A camera lens has a focal length...

Question 3

A meniscus lens is made with the radius of curvature of the convex surface being 25.0 cm and the concave surface 45.0 cm. If the glass used has index of refraction 1.50, what is the focal length of this lens?

Accepted Answer

The answer of A meniscus lens is made with the...

Question 4

A 4.0-cm-tall object is placed 50.0 cm from a diverging lens of focal length 25.0 cm. What is the nature and location of the image?

Accepted Answer

The answer of A 4.0-cm-tall object is placed 50.0 cm...

Question 5

An object is placed 100 cm in front of a diverging lens of focal length -25 cm. A converging lens of focal length  cm is placed 30 cm past the first lens. Where is the final image formed?

Accepted Answer

The answer of An object is placed 100 cm in...

Question 6

An object is placed on an optical bench. A lens with a focal length of 12 cm is placed 20 cm from the object. Where should a second lens, with a focal length of 4.0 cm, be placed if a total magnification +6 is to be obtained?

Accepted Answer

The total magnification is given by the product of the magnifications of the two lenses. The magnification of the first lens is -20/12 = -5/3, and the magnification of the second lens is 4/x, where x is the distance between the second lens and the object. The total magnification is therefore (-5/3)(4/x) = +6. Solving for x gives x = 35 cm.

Question 7

A meniscus lens is made with the radius of curvature of the convex surface being 45.0 cm and the concave surface 25.0 cm. If the glass used has index of refraction 1.50, what is the focal length of this lens?

Accepted Answer

The answer of A meniscus lens is made with the...

Question 8

A doubly convex thin lens is made of glass with an index of refraction of 1.52. The radii of curvature of the faces of the lens are 60 cm and 72 cm. What is the focal length of the lens?

Accepted Answer

The focal length of a lens can be calculated using the lensmaker's equation: 1/f = (n - 1) * (1/R1 - 1/R2). Substituting n = 1.52, R1 = 60 cm, and R2 = -72 cm (since the lens is convex on both sides), we find f ≈ 63 cm.

Question 9

A lens of focal length 25 cm is placed 50 cm from an object. On the opposite side of the lens at a distance of 50 cm is a plane mirror. Where is the final image formed?

Accepted Answer

The answer of A lens of focal length 25 cm...

Question 10

An object is placed 100 cm in front of a lens of focal length 20 cm. A second lens is placed 35 cm beyond the first, this second lens having a focal length of 8.0 cm. How far past the second lens is the final image formed?

Accepted Answer

The first lens forms an image 25 cm behind the first lens. The second lens then forms an image 15 cm behind the second lens.

Question 11

An object is placed on an optical bench. A lens with a focal length of 15 cm is placed 30 cm from the object. A diverging lens with a focal length of -10 cm is placed 7.0 cm beyond that. Where is the final image formed, relative to the second lens?

Accepted Answer

First, use the lens formula for the converging lens to find the image distance: 1/f = 1/v - 1/u, where f = 15 cm and u = -30 cm. This gives v = 30 cm. This image acts as the object for the diverging lens, with an object distance of 30 - 7 = 23 cm. Using the lens formula for the diverging lens with f = -10 cm, we find the final image distance v = -18 cm, meaning 18 cm behind the diverging lens.

Question 12

The focal length of a thin lens is 40 mm and its aperture diameter is 10 mm. What is the f-number of this lens?

Accepted Answer

The answer of The focal length of a thin lens...

Question 13

An object is placed 100 cm in front of a lens of focal length 20 cm. A second lens is placed 15 cm past the first lens. The second lens has a focal length of 40 cm. Where is the final image formed?

Accepted Answer

First, use the lens formula for the first lens to find the image distance: 1/f = 1/v - 1/u, where f = 20 cm and u = -100 cm. This gives v = 25 cm. The image from the first lens acts as the object for the second lens, located 25 - 15 = 10 cm in front of it. Using the lens formula for the second lens with f = 40 cm and u = -10 cm, the final image distance v is found to be 8 cm after the second lens.

Question 14

An object is placed 100 cm in front of a diverging lens of focal length -25 cm. A converging lens of focal length 33  cm is placed 30 cm past the first lens. What is the lateral magnification of this system of lenses?

Accepted Answer

The answer of An object is placed 100 cm in...

Question 15

An object is placed 100 cm in front of a lens of focal length 20 cm. A second lens is placed 35 cm beyond the first, this second lens having a focal length of 8.0 cm. If the size of the object is 6.0 cm, what is the size of the final image?

Accepted Answer

The answer of An object is placed 100 cm in...

Question 16

A lens of focal length 10.0 cm is placed in contact with another lens, the combination having a focal length of 20.0 cm. The focal length of the second lens is

Accepted Answer

The formula for the combined focal length of two lenses in contact is 1/F = 1/f1 + 1/f2. Given F = 20 cm and f1 = 10 cm, solving for f2 gives f2 = -20 cm.

Question 17

An object is placed 40 cm in front of a lens of focal length 40 cm. A second lens is placed 17 cm beyond the first. An image forms 48 cm past the second lens. The lateral magnification of this system is

Accepted Answer

The first lens forms an image at infinity since the object is at the focal point (40 cm). The second lens then forms an image 48 cm past it, with an object distance of 17 cm. The magnification of the second lens is -48/17 = -2.8. The total magnification is the product of the magnifications of the two lenses, which is 1 * -2.8 = -2.8. However, the question asks for lateral magnification, which is the absolute value, so the answer is 1.2.

Question 18

A lens is made with focal length -40 cm using a material with index of refraction 1.50. A second lens is made with the same geometry as the first but using a higher index material, the index being 2.00. What is the focal length of the second lens?

Accepted Answer

The answer of A lens is made with focal length...

Question 19

An object is placed 100 cm in front of a lens of focal length 50 cm. A lens of focal length -20 cm is placed 90 cm beyond the first lens. The final image is located

Accepted Answer

The answer of An object is placed 100 cm in...

Question 20

The focal length of the lens of a simple camera is 40.0 mm. How far must the lens be moved to change the focus of the camera from a person 25 m away to one that is 4.0 m away?

Accepted Answer

The answer of The focal length of the lens of...

Quiz 33: Lenses and Optical Instruments

What is the focal length of the corrective contact lens needed by a nearsighted person whose far point is 60 cm?

A camera lens has a focal length of 50.0 mm and an aperture setting of 4.00. What is the aperture diameter of this lens?

A meniscus lens is made with the radius of curvature of the convex surface being 25.0 cm and the concave surface 45.0 cm. If the glass used has index of refraction 1.50, what is the focal length of this lens?

A 4.0-cm-tall object is placed 50.0 cm from a diverging lens of focal length 25.0 cm. What is the nature and location of the image?

An object is placed 100 cm in front of a diverging lens of focal length -25 cm. A converging lens of focal length cm is placed 30 cm past the first lens. Where is the final image formed?

An object is placed on an optical bench. A lens with a focal length of 12 cm is placed 20 cm from the object. Where should a second lens, with a focal length of 4.0 cm, be placed if a total magnification +6 is to be obtained?

A meniscus lens is made with the radius of curvature of the convex surface being 45.0 cm and the concave surface 25.0 cm. If the glass used has index of refraction 1.50, what is the focal length of this lens?

A doubly convex thin lens is made of glass with an index of refraction of 1.52. The radii of curvature of the faces of the lens are 60 cm and 72 cm. What is the focal length of the lens?

A lens of focal length 25 cm is placed 50 cm from an object. On the opposite side of the lens at a distance of 50 cm is a plane mirror. Where is the final image formed?

An object is placed 100 cm in front of a lens of focal length 20 cm. A second lens is placed 35 cm beyond the first, this second lens having a focal length of 8.0 cm. How far past the second lens is the final image formed?

An object is placed on an optical bench. A lens with a focal length of 15 cm is placed 30 cm from the object. A diverging lens with a focal length of -10 cm is placed 7.0 cm beyond that. Where is the final image formed, relative to the second lens?

The focal length of a thin lens is 40 mm and its aperture diameter is 10 mm. What is the f-number of this lens?

An object is placed 100 cm in front of a lens of focal length 20 cm. A second lens is placed 15 cm past the first lens. The second lens has a focal length of 40 cm. Where is the final image formed?

An object is placed 100 cm in front of a diverging lens of focal length -25 cm. A converging lens of focal length 33 cm is placed 30 cm past the first lens. What is the lateral magnification of this system of lenses?

An object is placed 100 cm in front of a lens of focal length 20 cm. A second lens is placed 35 cm beyond the first, this second lens having a focal length of 8.0 cm. If the size of the object is 6.0 cm, what is the size of the final image?

A lens of focal length 10.0 cm is placed in contact with another lens, the combination having a focal length of 20.0 cm. The focal length of the second lens is

An object is placed 40 cm in front of a lens of focal length 40 cm. A second lens is placed 17 cm beyond the first. An image forms 48 cm past the second lens. The lateral magnification of this system is

A lens is made with focal length -40 cm using a material with index of refraction 1.50. A second lens is made with the same geometry as the first but using a higher index material, the index being 2.00. What is the focal length of the second lens?

An object is placed 100 cm in front of a lens of focal length 50 cm. A lens of focal length -20 cm is placed 90 cm beyond the first lens. The final image is located

The focal length of the lens of a simple camera is 40.0 mm. How far must the lens be moved to change the focus of the camera from a person 25 m away to one that is 4.0 m away?