The optical system of a toy refracting telescope consists of...

The optical system of a toy refracting telescope consists of a converging objective lens with a focal length of $20.0 \mathrm{cm},$ located $25.0 \mathrm{cm}$ from a converging eyepiece lens with a focal length of $4.05 \mathrm{cm} .$ The telescope is used to view a 10.0 -cm-high object, located $425 \mathrm{cm}$ from the objective lens. a. What are the image position, height, and orientation as formed by the objective lens? Is this a real or virtual image? b. The objective lens image becomes the object for the eyepiece lens. What are the image position, height, and orientation that a person sees when looking into the telescope? Is this a real or virtual image? c. What is the magnification of the telescope?

The optical system of a toy refracting telescope consists of a converging objective lens with a focal length of $20.0 \mathrm{cm},$ located $25.0 \mathrm{cm}$ from a converging eyepiece lens with a focal length of $4.05 \mathrm{cm} .$ The telescope is used to view a 10.0 -cm-high object, located $425 \mathrm{cm}$ from the objective lens.
a. What are the image position, height, and orientation as formed by the objective lens? Is this a real or virtual image?
b. The objective lens image becomes the object for the eyepiece lens. What are the image position, height, and orientation that a person sees when looking into the telescope? Is this a real or virtual image?
c. What is the magnification of the telescope?

Key Concepts

Lens Equation

The lens equation, often expressed as 1/f = 1/d_o + 1/d_i, is a fundamental relationship in geometric optics that links the focal length of a lens with the object distance and the image distance. This formula is used to determine where an image will form relative to a lens and whether the image will be real or virtual, which is essential in the analysis of optical systems such as telescopes.

Magnification

Magnification in optics relates the size of the image to the size of the object. It can be linear, as given by the ratio of image height to object height for a single lens, or angular, especially in telescopes where the overall magnification is the product of the magnifications provided by the individual lenses. Understanding magnification is crucial when examining how telescopes enhance the apparent size of distant objects.

Real vs Virtual Images

In optical systems, real images are formed when light rays converge and can be projected onto a screen, whereas virtual images are formed by rays that appear to diverge from a point behind the lens. This distinction is vital for determining the behavior and usability of optical instruments, including determining where an image can be observed in devices like telescopes.

Multiple Lens Systems

Multiple lens systems, such as those found in refracting telescopes, require a step-by-step analysis where the image formed by one lens serves as the object for the next lens. This approach is essential for understanding the overall imaging process, determining the final image characteristics, and calculating the total magnification of the system.

Image Orientation

Image orientation refers to whether an image is inverted or erect relative to the original object. In multi-element optical devices like telescopes, the arrangement of lenses often results in an inverted intermediate image, which then may become upright (or remain inverted) through further optical processing. This concept is important for both the practical usage of the instrument and the theoretical understanding of light behavior in lens systems.

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