第06章光的干涉习题答案.doc

第6章 光的干涉6.1 在杨氏双缝实验中，用钠光灯为光源已知光波长，屏幕距双缝的距离为，双缝的间距，求：第级明条纹到中心的距离；第级明条纹的宽度. 解：（1）明纹的条件： 暗纹的条件： 第4级明条纹得到中心的距离： （2）明条纹的宽度就是两相邻暗纹的间距： 6.2 在杨氏双缝实验中，用钠光灯为光源已知光波长，屏幕距双缝的距离为，问两种情况相邻明条纹间距分别为多大？若相邻条纹的最小分辨距离为，能分清干涉条纹的双缝间距最大是多少？解：（1）相邻两条强度最大值的条纹顶点间的距离为由此可知，当时当时（2）令能分清干涉条纹的双缝间距最大为d，则有6.3 用白光作光源观察杨氏双缝干涉设两缝的间距为，缝面与屏距离为，试求能观察到的清晰可见光谱的级次？解：白光波长在390750范围，为明纹的条件为在=0处，各种波长的光波程差均为零，所以各种波长的零级条纹在屏上处重叠形成中央白色条纹.中央明纹两侧，由于波长不同，同一级次的明纹会错开，靠近中央明纹的两侧，观察到的各种色光形成的彩色条纹在远处会重叠成白色条纹最先发生重叠的是某一级的红光 ，和高一级的紫光，因此从紫光到清晰可见光谱的级次可由下式求得：因而： 由于k只能取整数，因此从紫光到红光排列清晰可见的光谱只有正负各一级 6.4 在杨氏双缝干涉实验中，入射光的波长为，现在缝上放置一片厚度为，折射率为的透明介质，试问原来的零级明纹将如何移动？如果观测到零级明纹移到了原来的级明纹处，求该透明介质的厚度解：（1）原来的零级明纹将向那方移动。（2）如果观察到的零级条纹移动到了原来的k级明纹处则 6.5 在双缝干涉实验中，双缝间距，缝屏间距，若第二级明条纹离屏中心的距离为，试计算此单色光的波长解：令单色光的波长为，由为明条纹需要满足的条件可知，6.6 一束平面单色光垂直照射在厚度均匀的薄油膜上，油膜覆盖在玻璃上，油膜的折射率为6.6 一束平面单色光垂直照射在厚度均匀的薄油膜上，油膜覆盖在玻璃上，油膜的折射率为，玻璃的折射率为，若单色光的波长可由光源连续可调，可观察到与这两个波长的单色光在反射中消失试求油膜层的厚度解：由于油膜前后表面反射光都有半波损失，所以光程差为，而膜厚又是均匀的， 反射相消的条件是 ：反射消失在级，反射消失在级则有 因和应为正整数，则，。 因油膜干涉的效果主要是增透或者是显色，反射光最小，最小，对于油膜厚度最小，即取6.7 利用等厚干涉可测量微小的角度折射率的劈尖状板，在某单色光的垂直照射下，量出两相邻明条纹间距，已知单色光在空气中的波长，求劈尖顶角解：相长干涉的条件为相邻两条纹对应的薄膜厚度差为对于劈尖板，则条纹间距与相应的厚度变化之间的关系为6.8 用波长为的单色光，垂直照射长的两块玻璃片上，两玻璃片的一边互相接触，另一边夹着一块厚度为云母片，形成一个空气劈尖求： 两玻璃片间的夹角？相邻明条纹间空气膜的厚度差是多少？相邻两暗条纹的间距是多少？在这内呈现多少条明纹？解：（1）两玻璃间的夹角为（2）相邻两亮条纹对应的薄膜厚度差为 （3）条纹间距与相应厚度变化之间的关系 （4）在这0.12m内呈现的明条纹数为 当时，说明在这0.12 m内呈现了141条明条纹6.9 用的平行光垂直入射到劈形薄膜的上表面上，从反射光中观察，劈尖的棱边是暗纹若劈尖上面介质的折射率大于薄膜的折射率求：膜下面介质的折射率与的大小关系；第级暗纹处薄膜的厚度？使膜的下表面向下平移一微小距离，干涉条纹有什么样的变化？若，原来的第条暗纹处将被哪级暗纹占据？解：（1）（2）因为空气膜的上下都是玻璃，求反射光的光程差时应计入半波损失，处（棱）反射光相消，是暗条纹，从棱算到地条暗纹之间有各整条纹间隔，膜厚是的倍，（3）使膜的下表面向下平移一微小距离后，膜上表面向上平移，条纹疏密不变，整体向棱方向平移，原来地10条暗纹处的膜厚增加，干涉级增加 ： 因此原来的第条暗纹被第条暗纹代替6.10 白光垂直照射在空气中的厚度为的玻璃片上，玻璃的折射率为试问在可见光范围内（），哪些波长的光在反射中加强？哪些波长的光在透射中加强？解：（1）反射光加强的条件是： 当 在白光范围内反射光加强透射光加强的条件是： 当 在白光范围内时，透射光加强。 6.11 当牛顿环装置中的透镜与玻璃之间的空间充以液体时，第十个亮环的直径由变为，求液体的折射率？解：牛顿环干涉中，干涉条纹是以接触点为中心的同心圆环 明环半径为 原来透镜与玻璃板之间是空气，充液体后的折射率 因此液体的折射率为1.226.12 利用迈克耳逊干涉仪可测量单色光的波长，当可移动平面镜移动距离时，观察到干涉条纹移动数为条，求所用单色光的波长？解：移动平面镜后光程差变化为 6.13 反折射率为的玻璃片放入迈克耳逊干涉仪的一条光路中，观察到有条干涉条纹向一方移过若所用单色光的波长为，求此玻璃片的厚度解：设玻璃的厚度为 d放入玻璃片的光路中光程差变化为通过玻璃片的光程计算得到光线在玻璃片中的折射角所以光线在玻璃片的路程技术官员村位于位于亚运城东部，主干道二以东石楼涌以西的地块，占地面积、m2，总建筑面积、m2，共包括地下室南区、地下室北区、地上部分1栋12栋、服务中心、室外工程等多个单体工程。其中住宅面积m2，共12栋，17栋建筑层数为11层，812栋11层（局部复式顶层），首层局部架空，布置公建配套设施。integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and the second land of the seven hills. 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, old town-the South Bank Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, suspicious pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed, integrated energy, chemicals and textile Yibin city, are the three core pillars of the industry. In 2014, the wuliangye brand value to 73.58 billion yuan, the citys liquor industry slip to stabilise. Promoting deep development of integrated energy, advanced equipment manufacturing industry, changning district, shale gas production capacity reached 277 million cubic metres, built the countrys first independent high-yield wells and pipelines in the first section, the lead in factory production and supply to the population. 2.1-3 GDP growth figure 2.1-4 Yibin, Yibin city, Yibin city, fiscal revenue growth 2.1.4 topography terrain overall is Southwest, North-Eastern State. Low mountains and hills in the city landscape as the main ridge-and-Valley, pingba small fragmented nature picture for water and the second land of the seven hills. 236 meters to 2000 meters above sea level in the city, low mountain, 46.6% hills 45.3%, pingba only 8.1%. 2.1.5 development of Yibin landscapes and distinctive feature in the center of the city, with limitations, and spatial structure of typical zonal group, 2012-cities in building with an area of about 76.2km2. From city-building situation, old town-the South Bank Center construction is lagging behind, disintegration of the old city is slow, optimization and upgrading, quality public service resources are still heavily concentrated in the old town together. Southbank Centre has not been formed, functions of the service area space is missing. Meanwhile, peripheral group centres service was weak and inadequate accounting for city development, suspicious pattern could not be formed. As regards transport, with the outward expansion of cities, cities have been expanding, centripetal city traffic organization has not changed,