Light compound microscope with 15X eyepiece lens and 45X objective lens will have a magnification of:

Question

Accepted Answer

The correct option is 3:
The fundamental principle governing the magnifying power of a compound microscope, whether light or digital, is that the total magnification is the product of the magnifications of its two primary lens systems: the eyepiece (or ocular lens) and the objective lens. This is because the two lenses magnify the image in series. First, the objective lens creates an enlarged, real image of the specimen; second, the eyepiece lens then functions like a simple magnifier to further enlarge this image, which is now the intermediate image. The key formula we apply in this scenario is Total Magnification = Magnification of Eyepiece x Magnification of Objective. Given the parameters in the question—a 15X eyepiece lens and a 45X objective lens—we perform the straightforward arithmetic multiplication: 15 multiplied by 45. The result of this calculation is 675. Therefore, the microscope is capable of magnifying the specimen 675 times its actual size. This result is represented as 675X. Understanding this multiplicative rule is essential for correctly using a microscope and for selecting the appropriate lens combinations to achieve a desired level of detail and resolution for observing various cellular structures.

The incorrect option is 1:
The value 1000X, although a standard maximum magnification often achieved on many laboratory light microscopes, is not correct for the specific lens combination provided. 1000X is typically attained by pairing a 10X eyepiece with a 100X objective lens, which is the highest power found on conventional oil-immersion objectives. In our problem, the calculation $15 \times 45$ clearly does not equal 1000. Selecting 1000 suggests a misunderstanding of the question, perhaps confusing the calculated result with the common maximum capability of a different microscope setup. It serves as a reminder that magnification must be calculated from the lenses *actually* in use, not generalized maximum values.

The incorrect option is 2:
A total magnification of 2000X is substantially higher than the calculated value of 675X and is generally beyond the practical limit of resolution for a standard light compound microscope. While higher magnifications can technically be achieved by coupling stronger lenses (e.g., a 20X eyepiece with a 100X objective), 2000X often enters the territory where empty magnification occurs—an enlargement of the image without any increase in the discernible detail or resolution. This option is arithmetically incorrect, as the product of $15 \times 45$ is nowhere near 2000. Its selection likely stems from a major calculation error or an assumption that the microscope must achieve an extremely large, unrealistic magnification.

The incorrect option is 4:
The value 875X is mathematically incorrect for the given lens combination of 15X and 45X. The product of $15 \times 45$ is 675, not 875. This incorrect value may result from a simple calculation mistake, possibly from an error in multiplication or from attempting to add the numbers instead of multiplying them and then combining the terms with other missteps. For example, some students might perform an operation like $(15 \times 40) + 45 = 600 + 45 = 645$ or similar confused calculations. It is a value that is neither the correct product nor a common standard magnification found on microscopes, confirming its invalidity in this context.