An image is created by a 2 cm focal length concave mirror. The image is located 3 cm from the mirror. How far from the mirror is the object?

Question

BlackTom AI · Accepted Answer

We start by identifying the given data: a concave mirror with focal length f = +2 cm (positive for a concave mirror in standard sign convention), and an image distance v = +3 cm (positive, indicating a real image on the same side as the object).

Apply the mirror formula: 1/f = 1/u + 1/v, where u is the object distance (negative in the usual Cartesian sign convention, but we will solve for its magnitude and interpret the result for the distance from the mirror).

Plug in the known values: 1/2 = 1/u + 1/3.

Compute 1/u: 1/u = 1/2 − 1/3 = (3 − 2)/6 = 1/6, so u = 6 cm (magnitude).

Interpretation: the object is located 6 cm from the mirror. Since the distance is a positive magnitude and the sign convention yields u = −6 cm in the standard Cartesian system, the distance from the mirror is 6 cm.

Now evaluate each option:

- Option a: 6 cm — This matches the calculated object distance. It is the correct magnitude of how far the object sits from the mirror, given the provided f and v.
- Option b: 1 cm — This would imply a much larger image or a very different combination of f and v; it does not satisfy the mirror equation with f = 2 cm and v = 3 cm.
- Option c: 8 cm — If u were 8 cm, the left side 1/u would be 1/8, and 1/f would need to equal 1/8 + 1/3 = 11/24, which would give f ≈ 2.18 cm, not the given f = 2 cm, so this is inconsistent.
- Option d: 5 cm — If u were 5 cm, 1/u = 1/5, and 1/f would be 1/5 + 1/3 = 8/15, so f would be 15/8 ≈ 1.875 cm, which again does not match the given focal length of 2 cm.

In summary, only the 6 cm distance satisfies the mirror equation with f = 2 cm and v = 3 cm, while all other distances fail to reconcile the given focal length or image distance.

An image is created by a 2 cm focal length concave mirror. The image is located 3 cm from the mirror. How far from the mirror is the object?

查看解析

登录即可查看完整答案

类似问题

A 3.0 cm high object 5 cm from a convex mirror produces a virtual image. If the mirror has a focal length of 5 cm, what is height of the image?

With a 4 cm high object, positioned 12 cm away from a 4 cm focal length concave mirror, what is the height of the image?

An object is placed at a distance of 2f from a concave mirror of focal length f. The image distance is

A concave spherical mirror has a focal length of 20 cm. An object is placed 10 cm in front of the mirror on the mirror's axis. Where is the image located?

An object is located so that a virtual image is formed -8 cm behind a concave mirror that has a 7.9 cm focal length. Calculate the object distance.

An object is located so that a virtual image is formed -12.9 cm behind a concave mirror that has a 8 cm focal length. Calculate the object distance.

A convex mirror has a focal length of -20 cm. An object is placed 30 cm in front of the mirror. Determine the image distance, magnification, and image characteristics.

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单