{"id":840,"date":"2018-02-19T06:35:49","date_gmt":"2018-02-18T22:35:49","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=840"},"modified":"2018-02-19T06:35:49","modified_gmt":"2018-02-18T22:35:49","slug":"optical-instrument-magnifying-glass-problems-and-solutions","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/optical-instrument-magnifying-glass-problems-and-solutions.htm","title":{"rendered":"Optical instrument magnifying glass \u2013 problems and solutions","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. A 2 mm high object is placed 10 cm from a magnifying glass<\/a>. Near point N = 25 cm. Determine the angular magnification and image height.<\/span><\/span><\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

Object height (h<\/span><\/span>o<\/span><\/span><\/sub>) = 2 mm<\/span><\/span><\/p>\n

Near point (N) = 25 cm<\/span><\/span><\/p>\n

Object distance<\/a> (d<\/span><\/span>o<\/span><\/span><\/sub>) = 10 cm<\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> Angular magnification (M) and image height (h<\/span><\/span>i<\/span><\/span><\/sub>)<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

M = N \/ s<\/span><\/span><\/p>\n

M = 25 cm \/ 10 cm<\/span><\/span><\/p>\n

M = 2.5 <\/span><\/span><\/p>\n

The image height = 2.5 x 2 mm = 5 mm.<\/span><\/span><\/p>\n

2. A 25 cm focal length lens is used as magnifying glass. Determine (a) angular magnification when the eye<\/a> is focused at its near point N = 25 cm (b) angular magnification when the eye is relaxed.<\/span><\/span><\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

Near point (N) = 25 cm<\/span><\/span><\/p>\n

The focal length of a magnifying glass (f) = 25 cm <\/span><\/span><\/p>\n

The plus sign indicates that the lens is a converging lens.<\/i><\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/span><\/p>\n

(a) angular magnification when the eye is focused at its near point N = 25 cm<\/b><\/span><\/span><\/p>\n

M = (N\/f) + 1<\/span><\/span><\/p>\n

M = (25 cm \/ 25 cm) + 1<\/span><\/span><\/p>\n

M = 1 + 1<\/span><\/span><\/p>\n

M = 2 X<\/span><\/span><\/p>\n

If the object height is 1 cm, the image height is 2 x 1 cm = 2 cm. <\/span><\/span><\/p>\n

(b) angular magnification when the eye is relaxed<\/b><\/span><\/span><\/p>\n

M = N \/ f<\/span><\/span><\/p>\n

M = (25 cm \/ 25 cm) <\/span><\/span><\/p>\n

M = 1 X<\/span><\/span><\/p>\n

If the object height is 1 cm, the image height is 1 x 1 cm = 1 cm. <\/span><\/span><\/p>\n

3. A 1 cm high object is placed in front of a 10 cm focal length lens. Determine (a) the image height when the eye<\/a> is focused at its near point N = 25 cm (b) The image height when the eye is relaxed.<\/span><\/span><\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

The object height (h<\/span><\/span>o<\/span><\/span><\/sub>) = 1 cm<\/span><\/span><\/p>\n

The focal length (f) = 10 cm<\/span><\/span><\/p>\n

Near point (N) = 25 cm<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

(a) The image height when the eye is focused at its near point N = 25 cm<\/b><\/span><\/span><\/p>\n

M = (N\/f) + 1<\/span><\/span><\/p>\n

M = (25 cm \/ 10 cm) + 1<\/span><\/span><\/p>\n

M = 2.5 + 1<\/span><\/span><\/p>\n

M = 3.5 X<\/span><\/span><\/p>\n

If the object height is 1 cm, the image height is 3.5 x 1 cm = 3.5 cm. <\/span><\/span><\/p>\n

(b) The image height when the eye is relaxed.<\/b><\/span><\/span><\/p>\n

M = N\/f<\/span><\/span><\/p>\n

M = 25 cm \/ 10 cm <\/span><\/span><\/p>\n

M = 2.5 X<\/span><\/span><\/p>\n

If the object height is 1 cm, the image height is 2.5 x 1 cm = 2.5 cm. <\/span><\/span><\/p>\n

4. The angular magnification when the eye is relaxed = 5X. If near point = 25 cm, what is the focal length of the magnifying glass ?<\/span><\/span><\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

Object height (h<\/span><\/span>o<\/span><\/span><\/sub>) = 2 mm<\/span><\/span><\/p>\n

Angular magnification (M) = 5X<\/span><\/span><\/p>\n

Near point (N) = 25 cm<\/span><\/span><\/p>\n

Wanted:<\/u><\/span><\/span> The focal length <\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

The formula of the angular magnification when the eye is relaxed :<\/span><\/span><\/span><\/p>\n

M = N\/f<\/span><\/span><\/p>\n

5 = 25 cm \/ f <\/span><\/span><\/p>\n

f = 25 cm \/ 5<\/span><\/span><\/p>\n

f = 5 cm<\/span><\/span><\/p>\n

The focal length of the magnifying glass = 5 cm.<\/span><\/span><\/p>\n

5. <\/span><\/span>An object is seen by someone with a magnifying glass with the focal length is 15 cm. If the near point of the person’s eyes = 30 cm, then determine the overall magnification of the magnifying glass.<\/span><\/span><\/span><\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

The near point of the normal eye (N) = 30 cm<\/span><\/span><\/p>\n

The focal length of the magnifying glass (f) = 15 cm (plus sign because the glass is convergent) <\/span><\/span><\/p>\n

Wanted :<\/u><\/span><\/span> the maximum magnification<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

The maximum magnification occurs when the accommodation of eye is maximum. The angular magnification of the magnifying glass occurs when the accommodation of eye is maximum :<\/span><\/span><\/span><\/p>\n

M = (N\/f) + 1<\/span><\/span><\/p>\n

M = (30 cm \/ 15 cm) + 1<\/span><\/span><\/p>\n

M = 2 + 1<\/span><\/span><\/p>\n

M = 3<\/span><\/span> times<\/span><\/span><\/p>\n

6. A magnifying glass with the optical power 20 diopters used by a person with the normal eyes 25 cm. If the accommodation is minimum, determine the minimum magnification.<\/span><\/span><\/p>\n

Known :<\/u><\/span><\/span><\/p>\n

Near point of the normal eye (N) = 25 cm<\/span><\/span><\/p>\n

Power of the magnifying glass (P) = 20 diopters<\/span><\/span><\/p>\n

Wanted:<\/u><\/span><\/span> The minimum magnification<\/span><\/span><\/p>\n

Solution :<\/u><\/span><\/span><\/p>\n

The focal length of the magnifying glass :<\/span><\/span><\/p>\n

P = 1\/f <\/span><\/span><\/p>\n

20 = 1\/f<\/span><\/span><\/p>\n

f = 1\/20 <\/span><\/span><\/p>\n

f = 0.05 meters <\/span><\/span><\/p>\n

f = 5 cm<\/span><\/span><\/p>\n

The angular magnification when the accommodation is minimum :<\/span><\/span><\/p>\n

M = N \/ f<\/span><\/span><\/p>\n

M = (25 cm \/ 5 cm) <\/span><\/span><\/p>\n

M = 5 times<\/span><\/span><\/p>\n

[wpdm_package id=’872′]<\/p>\n

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    <\/p>\n

    \n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"excerpt":{"rendered":"

    1. A 2 mm high object is placed 10 cm from a magnifying glass. Near point N = 25 cm. Determine the angular magnification and image height. Known : Object height (ho) = 2 mm Near point (N) = 25 cm Object distance (do) = 10 cm Wanted : Angular magnification (M) and image height … Read more<\/a><\/p>\n","protected":false,"gt_translate_keys":[{"key":"rendered","format":"html"}]},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_seopress_titles_title":"","_seopress_titles_desc":"","_seopress_robots_index":"","_seopress_robots_follow":"","_seopress_robots_imageindex":"","_seopress_robots_snippet":"","_seopress_robots_primary_cat":"","_seopress_robots_breadcrumbs":"","_seopress_robots_freeze_modified_date":"","_seopress_robots_custom_modified_date":"","_seopress_robots_canonical":"","_seopress_social_fb_title":"","_seopress_social_fb_desc":"","_seopress_social_fb_img":"","_seopress_social_fb_img_attachment_id":0,"_seopress_social_fb_img_width":0,"_seopress_social_fb_img_height":0,"_seopress_social_twitter_title":"","_seopress_social_twitter_desc":"","_seopress_social_twitter_img":"","_seopress_social_twitter_img_attachment_id":0,"_seopress_social_twitter_img_width":0,"_seopress_social_twitter_img_height":0,"_seopress_redirections_value":"","_seopress_redirections_enabled":"","_seopress_redirections_enabled_regex":"","_seopress_redirections_logged_status":"","_seopress_redirections_param":"","_seopress_redirections_type":0,"_seopress_analysis_target_kw":"Optical instrument magnifying glass \u2013 problems and solutions","_seopress_news_disabled":"","_seopress_video_disabled":"","_seopress_video":[],"_seopress_pro_schemas_manual":[],"_seopress_pro_rich_snippets_disable_all":"","_seopress_pro_rich_snippets_disable":[],"_seopress_pro_schemas":[],"footnotes":""},"categories":[3],"tags":[],"class_list":["post-840","post","type-post","status-publish","format-standard","hentry","category-solved-problems-in-basic-physics"],"gt_translate_keys":[{"key":"link","format":"url"}],"_links":{"self":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/840","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/comments?post=840"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/840\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=840"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=840"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=840"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}