{"id":853,"date":"2018-02-19T10:04:06","date_gmt":"2018-02-19T02:04:06","guid":{"rendered":"https:\/\/gurumuda.net\/physics\/?p=853"},"modified":"2018-02-19T10:04:06","modified_gmt":"2018-02-19T02:04:06","slug":"optical-instrument-telescopes-problems-and-solution","status":"publish","type":"post","link":"https:\/\/gurumuda.net\/physics\/optical-instrument-telescopes-problems-and-solution.htm","title":{"rendered":"Optical instrument telescopes \u2013 problems and solution","gt_translate_keys":[{"key":"rendered","format":"text"}]},"content":{"rendered":"

1. <\/span><\/span>The focal length of the objective lens is 400 cm and the focal length of the ocular lens is 20 cm. If the eye<\/a> is relaxed, determine :<\/span><\/span><\/p>\n

a) <\/span><\/span>The overall magnification of telescope<\/a> (M)<\/span><\/span><\/p>\n

b) <\/span><\/span>the image distance from the objective lens <\/span><\/span>(<\/span><\/span>d<\/span><\/span>ob<\/span><\/sub>\u2019), <\/span><\/span><\/p>\n

c) <\/span><\/span>the image distance from the ocular lens<\/span><\/span> (<\/span><\/span>d<\/span><\/span>o<\/span>c<\/span><\/sub>) <\/span><\/span><\/p>\n

d) <\/span><\/span>the distance between the lenses<\/a><\/span><\/span><\/p>\n

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

The focal length of objective lens <\/span><\/span>(f<\/span><\/span>ob<\/span><\/sub>) = 400 cm<\/span><\/span><\/p>\n

The focal length of ocular lens (<\/span><\/span>f<\/span><\/span>o<\/span>c<\/span><\/sub>) = 20 cm<\/span><\/span><\/p>\n

The eye is relaxed so that <\/span><\/span>the real image generated by the objective lens is at the focal point of the objective lens and the first focal point of the ocular lens.<\/span><\/span><\/span><\/i><\/p>\n

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

a) <\/u><\/span><\/span>The overall magnification <\/u><\/span><\/span>(M)<\/u><\/span><\/span><\/p>\n

M = f<\/span><\/span>ob<\/span><\/sub> \/ f<\/span><\/span>o<\/span>c<\/span><\/sub><\/p>\n

M = 400 cm \/ 20 cm = 20<\/span><\/span>X<\/span><\/span><\/p>\n

The image is virtual and inverted. <\/span><\/span><\/p>\n

b) <\/u><\/span><\/span>The image distance from objective lens <\/u><\/span><\/span>(<\/u><\/span><\/span>d<\/u><\/span><\/span>ob<\/u><\/span><\/span><\/sub>\u2019)<\/u><\/span><\/span><\/p>\n

If the eye is relaxed, the image distance from objective lens <\/span><\/span>(<\/span><\/span>d<\/span><\/span>ob<\/span><\/sub>\u2019) = <\/span><\/span>the focal length of objective lens (<\/span><\/span>f<\/span><\/span>ob<\/span><\/sub>) = 400 cm = 4 m. <\/span><\/span><\/p>\n

c) <\/u><\/span><\/span>The distance of real image from the ocular lens <\/u><\/span><\/span>(<\/u><\/span><\/span>d<\/u><\/span><\/span>o<\/u><\/span>c<\/u><\/span><\/sub>)<\/u><\/span><\/span><\/p>\n

If the eye is relaxed, the distance of real image and ocular lens<\/span><\/span> (s<\/span><\/span>o<\/span>c<\/span><\/sub>) = <\/span><\/span>the focal length of ocular lens <\/span><\/span>(f<\/span><\/span>oc<\/span><\/sub>) = 20 cm = 0.2 m. <\/span><\/span><\/p>\n

d) <\/u><\/span><\/span>The distance between the lenses<\/u><\/span><\/span><\/p>\n

The distance between the lenses <\/span><\/span>= <\/span><\/span>the telescope length <\/span><\/span>(l) = <\/span><\/span>the focal length of objective lens <\/span><\/span>(f<\/span><\/span>ob<\/span><\/sub>) + <\/span><\/span>the focal length of ocular lens <\/span><\/span>(f<\/span><\/span>oc<\/span><\/sub>) = 400 cm + 20 cm = 420 cm. <\/span><\/span><\/p>\n

<\/p>\n

2. <\/span><\/span>The distance<\/a> between objective lens and ocular lens is 20 cm<\/span><\/span>. <\/span><\/span>The overall magnification of telescope when the eye is relaxed is 40X. Calculate the focal length of ocular lens<\/span><\/span> (f<\/span><\/span>o<\/span>c<\/span><\/sub>) <\/span><\/span>and the focal length of objective lens <\/span><\/span>(f<\/span><\/span>ob<\/span><\/sub>)<\/span><\/span><\/p>\n

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

the telescopes length <\/span><\/span>(l) = 20 cm<\/span><\/span><\/p>\n

the overall magnification of telescope <\/span><\/span>(M) = 40<\/span><\/span>X<\/span><\/span><\/p>\n

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

If the eye is relaxed, the focal length of ocular lens (f<\/span><\/span>oc<\/span><\/sub>) + the focal length of objective lens (f<\/span><\/span>ob<\/span><\/sub>) = the telescope length (l)<\/span><\/span><\/p>\n

f<\/span><\/span>o<\/span>c<\/span><\/sub> + f<\/span><\/span>ob<\/span><\/sub> = l <\/span><\/span><\/p>\n

f<\/span><\/span>ob<\/span><\/sub> = l – f<\/span><\/span>o<\/span>c<\/span><\/sub><\/p>\n

f<\/span><\/span>ob<\/span><\/sub> = 20 – f<\/span><\/span>o<\/span><\/span><\/sub>c<\/span><\/span><\/sub> —–> <\/span><\/span>equation 1<\/span><\/span><\/p>\n

The overall magnification of telescope <\/u><\/span><\/span>(M) :<\/u><\/span><\/span><\/p>\n

M = f<\/span><\/span>ob<\/span><\/sub> \/ f<\/span><\/span>o<\/span>c<\/span><\/sub><\/p>\n

f<\/span><\/span>ob<\/span><\/sub> = M f<\/span><\/span>o<\/span>c<\/span><\/sub><\/p>\n

f<\/span><\/span>ob<\/span><\/sub> = 40 f<\/span><\/span>o<\/span>c<\/span> <\/sub>—–> <\/span><\/span>equation 2<\/span><\/span><\/p>\n

The focal length of ocular lens <\/u><\/span><\/span>:<\/u><\/span><\/span><\/p>\n

Subtitute<\/span><\/span> f<\/span><\/span>ob<\/span><\/span><\/sub> in equation 1 with <\/span><\/span>f<\/span><\/span>ob<\/span><\/sub> in equation 2 :<\/span><\/span><\/p>\n

f<\/span><\/span>ob<\/span><\/sub> = 20 – f<\/span><\/span>o<\/span>c<\/span><\/sub><\/p>\n

40 f<\/span><\/span>o<\/span>c<\/span><\/sub> = 20 – f<\/span><\/span>o<\/span>c<\/span><\/sub><\/p>\n

40 f<\/span><\/span>o<\/span>c<\/span><\/sub> + f<\/span><\/span>o<\/span>c<\/span><\/sub> = 20<\/span><\/span><\/p>\n

41 f<\/span><\/span>o<\/span>c<\/span><\/sub> = 20<\/span><\/span><\/p>\n

f<\/span><\/span>o<\/span>c<\/span><\/sub> = 20 cm \/ 41 <\/span><\/span><\/p>\n

f<\/span><\/span>o<\/span>c<\/span><\/sub> = 0.5 cm<\/span><\/span><\/p>\n

The focal length of ocular lens = <\/span><\/span>0.5 cm.<\/span><\/span><\/p>\n

The focal length of the objective lens <\/u><\/span><\/span>:<\/u><\/span><\/span><\/p>\n

f<\/span><\/span>ob<\/span><\/sub> = 20 – f<\/span><\/span>oc<\/span><\/sub><\/p>\n

f<\/span><\/span>ob<\/span><\/sub> = 20 \u2013 0.5<\/span><\/span><\/p>\n

f<\/span><\/span>ob<\/span><\/sub> = 19.5 cm<\/span><\/span><\/p>\n

[wpdm_package id=’876′]<\/p>\n

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

    1. The focal length of the objective lens is 400 cm and the focal length of the ocular lens is 20 cm. If the eye is relaxed, determine : a) The overall magnification of telescope (M) b) the image distance from the objective lens (dob\u2019), c) the image distance from the ocular lens (doc) d) … 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 telescopes \u2013 problems and solution","_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-853","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\/853","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=853"}],"version-history":[{"count":0,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/posts\/853\/revisions"}],"wp:attachment":[{"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/media?parent=853"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/categories?post=853"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gurumuda.net\/physics\/wp-json\/wp\/v2\/tags?post=853"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}