Two mirrors are inclined by an angle `30^(@)`. An object is placed making `10^(@)` with the mirror My Find the positions of the first two images formed by each mirror. Find the total number of images.

Explanation

Figure is self explanatory.

Number of images
(i) Using direct formula
`360^(@)/30^(@)=12` (even number)
`:.` number of images `=12 -1 =11`
(ii) By counting

To check whether the final images made by the two mirrors coincide or not : add the last angles and the angle between the mirrors. If it comes out to be exactly `360^(@)`, it implies that the final images formed by the two mirrors coincide. Here last angles made by the mirrors + the angle between the mirrors `= 160^(@)+170^(@)+30^(@)=360^(@)`. Therefore in this case the last imagescoincide. Therefore the number of images = number of images formed by mirror `M_(1) +` number of images formed by mirror `M_(2)-1` (as the last images coincide) `=6+6-1=11`.