what do you understand by magnification of the image for virtual and real image
Answers
Linear magnification is calculated from the physical size of object and image, as measured by a ruler or similar linear measuring device. This is usually used with optical systems which provide a real image. Magnification is simply the size of the image divided by the size of the object that was magnified. Sometimes this is a signed quantity, where negative values indicate that the image is inverted with respect to the object, and sometimes only the absolute value is used.
Angular magnification is based on angular size, measured by a protractor or similar instrument. Angular size is always a measurement of size as observed from a particular position (often the pupil of your eye). Because it does not require a physical object or image to be measured, angular size and angular magnification can be calculated when the object is infinitely far away (e.g. the subject for an astro telescope) or when the image is virtual (e.g. when a lens is used as a magnifier). Angular magnification is the ratio of angular size of the image to the angular size of the object.
A telescope provides a good example of the use of angular magnification. Suppose that something appears to be 0.5 degree in size to your unaided eye, but appears to cover 10 degrees when you look at it through a telescope. Then the (angular) magnification of the telescope is 20 times. Linear magnification is not a useful measure for a telescope, both because the image in the eyepiece is virtual, and because the object size doesn’t really matter. The moon is 0.5 degree in size when viewed from Earth, but so is a small bird viewed from much closer, and the telescope magnifies the apparent size of both by 20 X.
A compound microscope is an interesting example of mixing linear and angular magnification. The objective lens of the microscope (or the objective plus the tube lens, in an infinity-corrected design) forms a real image within the microscope tube. The magnification marked on the objective is the linear magnification of this objective, when used with the microscope tube length or tube lens that the objective was intended to be used with. If the eyepiece contains a measuring reticle, or the scope contains a camera with its sensor located at the focus of the objective, the size of the image and the objective magnification can be used to calculate the true size of the object being observed.
However, the eyepiece of a microscope is used as a simple magnifier, which allows you to focus on the objective lens’ image from up close. The eyepiece itself produces a virtual image, not a real image. An eyepiece marked “10 X” simply means that its focal length is 25 mm, which allows you to see the intermediate image with an angular magnification of 10 compared to the (assumed) close focus limit of your unaided eye at 250 mm. So, when viewing with a 5 X objective and 10 X eyepiece, the overall (angular) magnification is 50 X, but that is made up of a linear magnification of 5 X from the objective, and an angular magnification of 10 X from the eyepiece.